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New sequence spaces derived by using generalized arithmetic divisor sum function and compact operators Forum Math. (IF 0.8) Pub Date : 2024-03-04 Taja Yaying, Nipen Saikia, Mohammad Mursaleen
Define an infinite matrix D α = ( d n , v α ) \mathfrak{D}^{\alpha}=(d^{\alpha}_{n,v}) by d n , v α = { v α σ ( α ) ( n ) , v ∣ n , 0 , v ∤ n , d^{\alpha}_{n,v}=\begin{cases}\dfrac{v^{\alpha}}{\sigma^{(\alpha)}(n)},&v\mid n,\\ 0,&v\nmid n,\end{cases} where σ ( α ) ( n ) \sigma^{(\alpha)}(n) is defined to be the sum of the 𝛼-th power of the positive divisors of n ∈ N n\in\mathbb{N} , and construct
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Building planar polygon spaces from the projective braid arrangement Forum Math. (IF 0.8) Pub Date : 2024-02-28 Navnath Daundkar, Priyavrat Deshpande
The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the moduli space of distinct points on the real projective line as an open dense subset. Kapranov showed that the real points of the Deligne–Mumford–Knudson compactification can be obtained from the projective Coxeter complex of type 𝐴 (equivalently, the projective braid
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q-supercongruences from Watson's 8φ7 transformation Forum Math. (IF 0.8) Pub Date : 2024-02-20 Xiaoxia Wang, Chang Xu
Employing Watson’s ϕ 7 8 {{}_{8}\phi_{7}} transformation formula, we unearth several q-supercongruences with a parameter s. Particularly, one of our results is an extension of a q-analogue of Van Hamme’s (G.2) supercongruence. In addition, we obtain a q-supercongruence modulo the fifth power of a cyclotomic polynomial and propose two related conjectures.
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Uniform bounds for Kloosterman sums of half-integral weight with applications Forum Math. (IF 0.8) Pub Date : 2024-02-20 Qihang Sun
Sums of Kloosterman sums have deep connections with the theory of modular forms, and their estimation has many important consequences. Kuznetsov used his famous trace formula and got a power-saving estimate with respect to x with implied constants depending on m and n. Recently, in 2009, Sarnak and Tsimerman obtained a bound uniformly in x, m and n. The generalized Kloosterman sums are defined with
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Orthogonal separation of variables for spaces of constant curvature Forum Math. (IF 0.8) Pub Date : 2024-02-20 Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as explicit formulas for the corresponding Killing tensors and Stäckel matrices.
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Joint distribution of the cokernels of random p-adic matrices II Forum Math. (IF 0.8) Pub Date : 2024-02-20 Jiwan Jung, Jungin Lee
In this paper, we study the combinatorial relations between the cokernels cok ( A n + p x i I n ) {\operatorname{cok}(A_{n}+px_{i}I_{n})} ( 1 ≤ i ≤ m {1\leq i\leq m} ), where A n {A_{n}} is an n × n {n\times n} matrix over the ring of p-adic integers ℤ p {\mathbb{Z}_{p}} , I n {I_{n}} is the n × n {n\times n} identity matrix and x 1 , … , x m {x_{1},\dots,x_{m}} are elements of ℤ p {\mathbb{Z}_{p}}
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Fundamental properties of Cauchy–Szegő projection on quaternionic Siegel upper half space and applications Forum Math. (IF 0.8) Pub Date : 2024-02-20 Der-Chen Chang, Xuan Thinh Duong, Ji Li, Wei Wang, Qingyan Wu
We investigate the Cauchy–Szegő projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy–Szegő kernel and prove that the Cauchy–Szegő kernel is nonzero everywhere, which further yields a non-degenerated pointwise lower bound. As applications, we prove the uniform boundedness of Cauchy–Szegő projection on every atom on the quaternionic
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Some properties of extended frame measure Forum Math. (IF 0.8) Pub Date : 2024-02-20 Jinjun Li, Zhiyi Wu, Fusheng Xiao
We prove that the extended frame spectral measures are of pure type and the Beurling dimension of any frame measure for an extended frame spectral measure is in its Fourier dimension and upper entropy dimension.
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Submodules of normalisers in groupoid C*-algebras and discrete group coactions Forum Math. (IF 0.8) Pub Date : 2024-02-20 Fuyuta Komura
In this paper, we investigate certain submodules in C*-algebras associated to effective étale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of compactly supported continuous functions on some open set. As a corollary, we show that discrete group coactions on groupoid C*-algebras are induced by cocycles of étale groupoids if the fixed point algebras contain
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Normalized solutions for the fractional Schrödinger equation with combined nonlinearities Forum Math. (IF 0.8) Pub Date : 2024-01-31 Shengbing Deng, Qiaoran Wu
In this paper, we study the normalized solutions for the following fractional Schrödinger equation with combined nonlinearities { ( - Δ ) s u = λ u + μ | u | q - 2 u + | u | p - 2 u in ℝ N , ∫ ℝ N u 2 𝑑 x = a 2 , \displaystyle\left\{\begin{aligned} \displaystyle{}(-\Delta)^{s}u&% \displaystyle=\lambda u+\mu\lvert u\rvert^{q-2}u+\lvert u\rvert^{p-2}u&&% \displaystyle\phantom{}\text{in
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The C*-algebra of the Boidol group Forum Math. (IF 0.8) Pub Date : 2024-01-31 Ying-Fen Lin, Jean Ludwig
The Boidol group is the smallest non- ∗ {\ast} -regular exponential Lie group. It is of dimension 4 and its Lie algebra is an extension of the Heisenberg Lie algebra by the reals with the roots 1 and -1. We describe the C*-algebra of the Boidol group as an algebra of operator fields defined over the spectrum of the group. It is the only connected solvable Lie group of dimension less than or equal to
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Cellular covers of divisible uniserial modules over valuation domains Forum Math. (IF 0.8) Pub Date : 2024-01-31 László Fuchs, Brendan Goldsmith, Luigi Salce, Lutz Strüngmann
Cellular covers which originate in homotopy theory are considered here for a very special class: divisible uniserial modules over valuation domains. This is a continuation of the study of cellular covers of divisible objects, but in order to obtain more substantial results, we are restricting our attention further to specific covers or to specific kernels. In particular, for h-divisible uniserial modules
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Profinite genus of fundamental groups of compact flat manifolds with the cyclic holonomy group of square-free order Forum Math. (IF 0.8) Pub Date : 2024-01-31 Genildo de Jesus Nery
In this article, we study the extent to which an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a formula for the cardinality of profinite genus of the fundamental group of an n-dimensional compact flat manifold with the cyclic holonomy group of square-free order
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Degrees of generalized Kloosterman sums Forum Math. (IF 0.8) Pub Date : 2024-01-30 Liping Yang
The modern study of the exponential sums is mainly about their analytic estimates as complex numbers, which is local. In this paper, we study one global property of the exponential sums by viewing them as algebraic integers. For a kind of generalized Kloosterman sums, we present their degrees as algebraic integers.
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Bi-parameter and bilinear Calderón–Vaillancourt theorem with critical order Forum Math. (IF 0.8) Pub Date : 2024-01-30 Jiao Chen, Liang Huang, Guozhen Lu
In this paper, we establish the sharp Calderón–Vaillancourt theorem on L p L^{p} spaces for bi-parameter and bilinear pseudo-differential operators with symbols of critical order by deriving a sufficient and necessary condition on its symbol. This sharpens the result of [G. Lu and L. Zhang, Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order, Forum Math. 28 2016, 6, 1087–1094]
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Algebraic results on rngs of singular functions Forum Math. (IF 0.8) Pub Date : 2024-01-30 Arran Fernandez, Müge Saadetoğlu
We consider a Mikusiński-type convolution algebra C α {C_{\alpha}} , including functions with power-type singularities at the origin as well as all functions continuous on [ 0 , ∞ ) {[0,\infty)} . Algebraic properties of this space are derived, including its ideal structure, filtered and graded structure, and Jacobson radical. Applications to operators of fractional calculus and the associated integro-differential
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Hardy inequalities on metric measure spaces, IV: The case p=1 Forum Math. (IF 0.8) Pub Date : 2024-01-14 Michael Ruzhansky, Anjali Shriwastawa, Bankteshwar Tiwari
In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case p = 1 {p=1} and 1 ≤ q < ∞ {1\leq q<\infty} . This result complements the Hardy inequalities obtained in [M. Ruzhansky and D. Verma, Hardy inequalities on metric measure spaces, Proc. Roy. Soc. A. 475 2019, 2223, Article ID 20180310] in the case 1 < p ≤ q < ∞ {1 1 {p>1}
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Transcendence on algebraic groups Forum Math. (IF 0.8) Pub Date : 2024-01-10 Duc Hiep Pham
In this paper, we give some new results on transcendence on algebraic groups. These results extend some previous ones established on commutative or linear algebraic groups to arbitrary algebraic groups in complex and p-adic fields, respectively.
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Supercongruences arising from a 7 F 6 hypergeometric transformation formula Forum Math. (IF 0.8) Pub Date : 2024-01-10 Chen Wang
Using a F 6 7 {{}_{7}F_{6}} hypergeometric transformation formula, we prove two supercongruences. In particular, one of these supercongruences confirms a recent conjecture of Guo, Liu and Schlosser, and gives an extension of a supercongruence of Long and Ramakrishna.
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An explicit version of Bombieri’s log-free density estimate and Sárközy’s theorem for shifted primes Forum Math. (IF 0.8) Pub Date : 2024-01-10 Jesse Thorner, Asif Zaman
We make explicit Bombieri’s refinement of Gallagher’s log-free “large sieve density estimate near σ = 1 {\sigma=1} ” for Dirichlet L-functions. We use this estimate and recent work of Green to prove that if N ≥ 2 {N\geq 2} is an integer, A ⊆ { 1 , … , N } {A\subseteq\{1,\ldots,N\}} , and for all primes p no two elements in A differ by p - 1 {p-1} , then | A | ≪ N 1 - 10 - 18 {|A|\ll N^{1-10^{-18}}}
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Multiple normalized solutions for fractional elliptic problems Forum Math. (IF 0.8) Pub Date : 2024-01-10 Thin Van Nguyen, Vicenţiu D. Rădulescu
In this article, we are first concerned with the existence of multiple normalized solutions to the following fractional p-Laplace problem: { ( - Δ ) p s v + 𝒱 ( ξ x ) | v | p - 2 v = λ | v | p - 2 v + f ( v ) in ℝ N , ∫ ℝ N | v | p 𝑑 x = a p , \left\{\begin{aligned} \displaystyle{}(-\Delta)_{p}^{s}v+\mathcal{V}(\xi x)% \lvert v\rvert^{p-2}v&\displaystyle=\lambda\lvert v\rvert^{p-2}v+f(v)\quad%
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Topological amenability of semihypergroups Forum Math. (IF 0.8) Pub Date : 2024-01-05 Choiti Bandyopadhyay
In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of convergence of certain probability measures, total variation of convolution with probability measures and translation of certain functionals, as well as the F-algebraic
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What conjugate phase retrieval complex vectors can do in quaternion Euclidean spaces Forum Math. (IF 0.8) Pub Date : 2024-01-05 Yun-Zhang Li, Ming Yang
Quaternion algebra ℍ {\mathbb{H}} is a noncommutative associative algebra. In recent years, quaternionic Fourier analysis has received increasing attention due to its applications in signal analysis and image processing. This paper addresses conjugate phase retrieval problem in the quaternion Euclidean space ℍ M {\mathbb{H}^{M}} with M ≥ 2 {M\geq 2} . Write ℂ η = { ξ : ξ = ξ 0 + β η , ξ 0 , β ∈ ℝ
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Wells-type exact sequence and crossed extensions of algebras with bracket Forum Math. (IF 0.8) Pub Date : 2024-01-05 José Manuel Casas, Emzar Khmaladze, Manuel Ladra
We study the extensibility problem of a pair of derivations associated with an abelian extension of algebras with bracket, and derive an exact sequence of the Wells type. We introduce crossed modules for algebras with bracket and prove their equivalence with internal categories in the category of algebras with bracket. We interpret the set of equivalence classes of crossed extensions as the second
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Topological embeddings into transformation monoids Forum Math. (IF 0.8) Pub Date : 2024-01-05 Serhii Bardyla, Luke Elliott, James D. Mitchell, Yann Péresse
In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid ℕ ℕ {\mathbb{N}^{\mathbb{N}}} or the symmetric inverse monoid I ℕ {I_{\mathbb{N}}} with their respective canonical Polish semigroup topologies. We characterise those topological semigroups that embed topologically into ℕ ℕ {\mathbb{N}^{\mathbb{N}}} and belong to any of the
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Multilinear Fourier integral operators on modulation spaces Forum Math. (IF 0.8) Pub Date : 2024-01-04 Aparajita Dasgupta, Lalit Mohan, Shyam Swarup Mondal
In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of weighted modulation spaces. Further, we investigate the periodic multilinear Fourier integral operator. Finally, we study continuity of bilinear pseudo-differential
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Archimedean toroidal maps and their edge covers Forum Math. (IF 0.8) Pub Date : 2024-01-01 Arnab Kundu, Dipendu Maity
The automorphism group of a map on a surface acts naturally on its flags (triples of incident vertices, edges, and faces). We will study the action of the automorphism group of a map on its edges. A map is semi-equivelar if all of its vertices have the same type of face-cycles. A semi-equivelar toroidal map refers to a semi-equivelar map embedded on a torus. If a map has k edge orbits under its automorphism
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Finite approximation properties of C*-modules III Forum Math. (IF 0.8) Pub Date : 2024-01-01 Massoud Amini
We introduce and study a notion of module nuclear dimension for a C * \mathrm{C}^{*} -algebra A which is a C * \mathrm{C}^{*} -module over another C * \mathrm{C}^{*} -algebra 𝔄 {\mathfrak{A}} with compatible actions. We show that the module nuclear dimension of A is zero if A is 𝔄 {\mathfrak{A}} -NF. The converse is shown to hold when 𝔄 {\mathfrak{A}} is a C ( X ) {C(X)} -algebra with simple fibers
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Tilings of the sphere by congruent quadrilaterals III: Edge combination a 3 b with general angles Forum Math. (IF 0.8) Pub Date : 2024-01-01 Yixi Liao, Pinren Qian, Erxiao Wang, Yingyun Xu
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of a 3 b {a^{3}b} -quadrilaterals with some irrational angle: there are a sequence of 1-parameter families of quadrilaterals admitting 2-layer earth map tilings together with their basic flip modifications under extra condition, and 5 sporadic quadrilaterals
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On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center Forum Math. (IF 0.8) Pub Date : 2024-01-01 Diego García-Lucas, Leo Margolis
We show that the modular isomorphism problem has a positive answer for groups of nilpotency class 2 with cyclic center, i.e., that for such p-groups G and H an isomorphism between the group algebras FG and FH implies an isomorphism of the groups G and H for F the field of p elements. For groups of odd order this implication is also proven for F being any field of characteristic p. For groups of even
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L-series of weakly holomorphic quasimodular forms and a converse theorem Forum Math. (IF 0.8) Pub Date : 2024-01-01 Mrityunjoy Charan
We define L-series of weakly holomorphic quasimodular forms and we derive functional equations of those L-series. We also prove a converse theorem for weakly holomorphic quasimodular forms.
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Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications Forum Math. (IF 0.8) Pub Date : 2024-01-01 João Marcos do Ó, Guozhen Lu, Raoní Ponciano
We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths
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Two curious q-supercongruences and their extensions Forum Math. (IF 0.8) Pub Date : 2024-01-01 Haihong He, Xiaoxia Wang
We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of the q-binomial theorem, a Karlsson–Minton-type summation formula due to Gasper, and the method of “creative microscoping” developed by Guo and Zudilin. Incidentally, an assertion of Li, Tang
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A note on the post quantum-Sheffer polynomial sequences Forum Math. (IF 0.8) Pub Date : 2024-01-01 Subuhi Khan, Mehnaz Haneef
In this article, the post quantum analogue of Sheffer polynomial sequences is introduced using concepts of post quantum calculus. The series representation, recurrence relations, determinant expression and certain other properties of this class are established. Further, the 2D-post quantum-Sheffer polynomials are introduced via generating function and their properties are established. Certain identities
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Generalized orthogonal measures on the space of unital completely positive maps Forum Math. (IF 0.8) Pub Date : 2024-01-01 Angshuman Bhattacharya, Chaitanya J. Kulkarni
A classical result by Effros connects the barycentric decomposition of a state on a C*-algebra to the disintegration theory of the GNS representation of the state with respect to an orthogonal measure on the state space of the C*-algebra. In this note, we take this approach to the space of unital completely positive maps on a C*-algebra with values in B ( H ) {B(H)} , connecting the barycentric decomposition
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Octonionic monogenic and slice monogenic Hardy and Bergman spaces Forum Math. (IF 0.8) Pub Date : 2024-01-01 Fabrizio Colombo, Rolf Sören Kraußhar, Irene Sabadini
In this paper we discuss some basic properties of octonionic Bergman and Hardy spaces. In the first part we review some fundamental concepts of the general theory of octonionic Hardy and Bergman spaces together with related reproducing kernel functions in the monogenic setting. We explain how some of the fundamental problems in well-defining a reproducing kernel can be overcome in the non-associative
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A fixed point theorem for isometries on a metric space Forum Math. (IF 0.8) Pub Date : 2024-01-01 Andrzej Wiśnicki
We show that if X is a complete metric space with uniform relative normal structure and G is a subgroup of the isometry group of X with bounded orbits, then there is a point in X fixed by every isometry in G. As a corollary, we obtain a theorem of U. Lang (2013) concerning injective metric spaces. A few applications of this theorem are given to the problems of inner derivations. In particular, we show
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One-sided Gorenstein rings Forum Math. (IF 0.8) Pub Date : 2024-01-01 Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, Junpeng Wang
Distinctive characteristics of Iwanaga–Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein global dimensions carry over to the one-sided situation, even without the noetherian hypothesis. Our results yield new relations among homological invariants related to the Gorenstein property, not only Gorenstein global dimensions
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Multiplicity of solutions for a singular system with sign-changing potential Forum Math. (IF 0.8) Pub Date : 2024-01-01 Wentao Lin, Yilan Wei
This paper focuses on a singular system with a sign-changing potential in Γ, a bounded domain with a Lipschitz boundary in ℝ d {\mathbb{R}^{d}} . By imposing appropriate conditions on the weight potential, which is allowed to change sign, we establish the existence of multiple solutions using the shape optimization approach. This study represents one of the earliest endeavors to explore and analyze
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Finite rigid sets of the non-separating curve complex Forum Math. (IF 0.8) Pub Date : 2024-01-01 Rodrigo De Pool
We prove that the non-separating curve complex of every surface of finite type and genus at least three admits an exhaustion by finite rigid sets.
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Donoho–Stark and Price uncertainty principles for a class of q-integral transforms with bounded kernels Forum Math. (IF 0.8) Pub Date : 2024-01-01 Luis P. Castro, Rita C. Guerra
We consider a very global q-integral transform, essentially characterized by having a bounded kernel and satisfying a set of natural and useful properties for the realization of applications. The main ambition of this work is to seek conditions that guarantee uncertainty principles of the Donoho–Stark type for that class of q-integral transforms. It should be noted that the global character of the
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Enochs’ conjecture for cotorsion pairs and more Forum Math. (IF 0.8) Pub Date : 2024-01-01 Silvana Bazzoni, Jan Šaroch
Enochs’ conjecture asserts that each covering class of modules (over any ring) has to be closed under direct limits. Although various special cases of the conjecture have been verified, the conjecture remains open in its full generality. In this paper, we prove the conjecture for the classes Filt ( 𝒮 ) {\operatorname{Filt}(\mathcal{S})} , where 𝒮 {\mathcal{S}} consists of ℵ n {\aleph_{n}} -presented
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The quotient set of the quadratic distance set over finite fields Forum Math. (IF 0.8) Pub Date : 2024-01-01 Alex Iosevich, Doowon Koh, Firdavs Rakhmonov
Let 𝔽 q d {\mathbb{F}_{q}^{d}} be the d-dimensional vector space over the finite field 𝔽 q {\mathbb{F}_{q}} with q elements. For each non-zero r in 𝔽 q {\mathbb{F}_{q}} and E ⊂ 𝔽 q d {E\subset\mathbb{F}_{q}^{d}} , we define W ( r ) {W(r)} as the number of quadruples ( x , y , z , w ) ∈ E 4 {(x,y,z,w)\in E^{4}} such that Q ( x - y ) Q ( z - w ) = r {\frac{Q(x-y)}{Q(z-w)}=r} , where Q is a
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The globally smooth solutions and asymptotic behavior of the nonlinear wave equations in dimension one with multiple speeds Forum Math. (IF 0.8) Pub Date : 2024-01-01 Changhua Wei
We are interested in the one-dimensional nonlinear wave equations with multiple wave speeds by the energy method. By choosing different multipliers corresponding to the different wave speeds, we show that the one-dimensional nonlinear wave equations also have globally smooth solutions provided that the nonlinearities satisfy certain structural conditions when the initial data are small. Furthermore
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Regularity of fractional heat semigroups associated with Schrödinger operators on Heisenberg groups Forum Math. (IF 0.8) Pub Date : 2024-01-01 Chuanhong Sun, Pengtao Li, Zengjian Lou
Let L = - Δ ℍ n + V {L=-{\Delta}_{\mathbb{H}^{n}}+V} be a Schrödinger operator on Heisenberg groups ℍ n {\mathbb{H}^{n}} , where Δ ℍ n {{\Delta}_{\mathbb{H}^{n}}} is the sub-Laplacian, the nonnegative potential V belongs to the reverse Hölder class B 𝒬 / 2 {B_{\mathcal{Q}/2}} . Here 𝒬 {\mathcal{Q}} is the homogeneous dimension of ℍ n {\mathbb{H}^{n}} . In this article, we introduce the fractional
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The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras Forum Math. (IF 0.8) Pub Date : 2024-01-01 Dirceu Bagio, Daniel Gonçalves, Paula Savana Estácio Moreira, Johan Öinert
Given a partial action α of a groupoid G on a ring R, we study the associated partial skew groupoid ring R ⋊ α G {R\rtimes_{\alpha}G} , which carries a natural G-grading. We show that there is a one-to-one correspondence between the G-invariant ideals of R and the graded ideals of the G-graded ring R ⋊ α G {R\rtimes_{\alpha}G} . We provide sufficient conditions for primeness, and necessary and sufficient
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Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators Forum Math. (IF 0.8) Pub Date : 2024-01-01 Karlheinz Gröchenig, Christine Pfeuffer, Joachim Toft
We extend the stability and spectral invariance of convolution-dominated matrices to the case of quasi-Banach algebras p < 1 {p<1} . As an application, we construct a spectrally invariant quasi-Banach algebra of pseudodifferential operators with non-smooth symbols that generalize Sjöstrand’s results.
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Improved spectral cluster bounds for orthonormal systems Forum Math. (IF 0.8) Pub Date : 2023-12-14 Tianyi Ren, An Zhang
We improve the work [R. L. Frank and J. Sabin, Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces, Adv. Math. 317 2017, 157–192] concerning the spectral cluster bounds for orthonormal systems at p = ∞ {p=\infty} , on the flat torus and spaces of nonpositive sectional curvature, by shrinking the spectral band from [ λ 2 , ( λ + 1 ) 2 ) {[\lambda^{2}
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Positive rigs Forum Math. (IF 0.8) Pub Date : 2023-11-29 Matías Menni
A positive rig is a commutative and unitary semi-ring A such that 1 + x {1+x} is invertible for every x ∈ A {x\in A} . We show that the category of positive rigs shares many properties with that of K-algebras for a (non-algebraically closed) field K. In particular, it is coextensive and, although we do not have an analogue of Hilbert’s basis theorem for positive rigs, we show that every finitely presentable
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The Eisenstein cycles and Manin–Drinfeld properties Forum Math. (IF 0.8) Pub Date : 2023-11-29 Debargha Banerjee, Loïc Merel
Let Γ be a subgroup of finite index of SL 2 ( 𝐙 ) {\operatorname{SL}_{2}(\mathbf{Z})} . We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian J Γ {J_{\Gamma}} of the corresponding modular curve X Γ {X_{\Gamma}} . Our main tool is the explicit description, in terms of modular symbols, of what we call Eisenstein cycles. The latter are representations of relative homology
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Stability of solutions to obstacle problems with generalized Orlicz growth Forum Math. (IF 0.8) Pub Date : 2023-11-29 Petteri Harjulehto, Arttu Karppinen
We consider nonlinear equations having generalized Orlicz growth (also known as Musielak–Orlicz growth). We prove that if differential operators 𝒜 i {\mathcal{A}_{i}} converge locally uniformly to an operator 𝒜 {\mathcal{A}} , then the sequence of solutions ( u i ) {(u_{i})} has a subsequence converging to the solution u of the limit operator in Sobolev and Hölder norms.
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A note on the essential numerical range of block diagonal operators Forum Math. (IF 0.8) Pub Date : 2023-11-29 Luís Carvalho, Cristina Diogo, Sérgio Mendes, Helena Soares
In this note, we characterize the essential numerical range of a block diagonal operator T = ⊕ i T i {T=\bigoplus_{i}T_{i}} in terms of the numerical ranges { W ( T i ) } i {\{W(T_{i})\}_{i}} of its components. Specifically, the essential numerical range of T is the convex hull of the limit superior of { W ( T i ) } i {\{W(T_{i})\}_{i}} . This characterization can be simplified further. In fact
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On abelian-by-cyclic Moufang loops Forum Math. (IF 0.8) Pub Date : 2023-11-29 Aleš Drápal, Petr Vojtěchovský
We initiate a systematic study of abelian-by-cyclic Moufang loops, that is, Moufang loops Q with an abelian normal subgroup X such that Q / X {Q/X} is a cyclic group. Among other results, we construct all split abelian-by-cyclic Moufang loops in which both X and Q / X {Q/X} are 3-divisible, using so-called Moufang permutations on X, which are permutations that deviate from an automorphism of X by an
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Global classical solution of the Cauchy problem to the 3D Benjamin–Bona–Mahony–Burgers-type equation with nonlocal control constraints Forum Math. (IF 0.8) Pub Date : 2023-11-29 Wenbing Wu
This article focuses on the Cauchy problem of the Benjamin–Bona–Mahony–Burgers (BBMB) equation with nonlocal control constraints in ℝ 3 {\mathbb{R}^{3}} . We employ the Phragmén–Lindelöf decomposition method and Green’s function to investigate global classical solutions and their long-term behaviors, including optimal estimates for finite density initial perturbation. Additionally, optimal solutions
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Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2 Forum Math. (IF 0.8) Pub Date : 2023-11-29 Yao Yuan
Let M ( d , χ ) {M(d,\chi)} , with ( d , χ ) = 1 {(d,\chi)=1} , be the moduli space of semistable sheaves on ℙ 2 {\mathbb{P}^{2}} supported on curves of degree d and with Euler characteristic χ. The cohomology ring H * ( M ( d , χ ) , ℤ ) {H^{*}(M(d,\chi),\mathbb{Z})} of M ( d , χ ) {M(d,\chi)} is isomorphic to its Chow ring A * ( M ( d , χ ) ) {A^{*}(M(d,\chi))} by Markman’s result. Pi
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Schauder estimates for Bessel operators Forum Math. (IF 0.8) Pub Date : 2023-11-19 Giorgio Metafune, Luigi Negro, Chiara Spina
We prove Schauder estimates for elliptic and parabolic problems governed by the degenerate operator ℒ = Δ x + D y y + c y D y , \mathcal{L}=\Delta_{x}+D_{yy}+\frac{c}{y}D_{y}, in the half-space Ω = { ( x , y ) : x ∈ ℝ N , y > 0 } {\Omega=\{(x,y):x\in\mathbb{R}^{N},y>0\}} , under Neumann boundary conditions at y = 0 {y=0} .
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On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems Forum Math. (IF 0.8) Pub Date : 2023-10-26 Prashanta Garain, Wontae Kim, Juha Kinnunen
We establish existence results for a class of mixed anisotropic and nonlocal p-Laplace equations with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To this end, we also discuss the necessary regularity properties of weak solutions of the associated non-singular problems. More precisely, we obtain local boundedness
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The smallest Mealy automaton generating an indicable regular branch group Forum Math. (IF 0.8) Pub Date : 2023-10-26 Adam Woryna
We construct a two-state Mealy automaton A over the three-letter alphabet generating a regular branch group G ( A ) {G(A)} , which surjects onto the infinite cyclic group. Some algebraic and geometric properties of the group G ( A ) {G(A)} are derived. In particular, this group has a nearly finitary subgroup of index two, is amenable, just non-solvable, has exponential growth, and its action on
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Simple 𝔰𝔩 d+1-modules from Witt algebra modules Forum Math. (IF 0.8) Pub Date : 2023-10-26 Xiangqian Guo, Xuewen Liu, Fenghua Zhang
Let d ≥ 1 {d\geq 1} be an integer and let 𝒲 d {\mathcal{W}_{d}} be the Witt algebra. For any admissible 𝒲 d {\mathcal{W}_{d}} -module P and any 𝔤 𝔩 d {\mathfrak{gl}_{d}} -module V, one can form a 𝒲 d {\mathcal{W}_{d}} -module ℱ ( P , V ) {\mathcal{F}(P,V)} , which as a vector space is P ⊗ V {P\otimes V} . Since 𝒲 d {\mathcal{W}_{d}} has a natural subalgebra isomorphic to 𝔰 𝔩 d + 1 {\mathfrak{sl}_{d+1}}
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Open orbits and primitive zero ideals for solvable Lie algebras Forum Math. (IF 0.8) Pub Date : 2023-10-26 Ali Baklouti, Hideyuki Ishi
The aim of the paper is to provide a characterization criterion of exponential solvable Frobenius Lie algebras (having open coadjoint orbits), in terms of primitive ideals of the associated enveloping algebra. In the case of complex solvable Lie algebras, we also show that an algebraic adjoint orbit is open if and only if the associated primitive ideal through the Dixmier map is trivial.