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New results on spectral synthesis Monatshefte Math. (IF 0.9) Pub Date : 2024-03-13 László Székelyhidi
In our former paper we introduced the concept of localization of ideals in the Fourier algebra of a locally compact Abelian group. It turns out that localizability of a closed ideal in the Fourier algebra is equivalent to the synthesizability of the annihilator of that closed ideal which corresponds to this ideal in the measure algebra. This equivalence provides an effective tool to prove synthesizability
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Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions Monatshefte Math. (IF 0.9) Pub Date : 2024-03-12 Guangshi Lü, Qiang Ma
We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg L-functions attached to two cuspidal automorphic representations.
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On a construction method of new moment sequences Monatshefte Math. (IF 0.9) Pub Date : 2024-03-05 Seunghwan Baek, Hayoung Choi, Seonguk Yoo
In this paper we provide a way to construct new moment sequences from a given moment sequence. An operator based on multivariate positive polynomials is applied to get new moment sequences. A class of new sequences is corresponding to a unique symmetric polynomial; if this polynomial is positive, then the new sequence becomes again a moment sequence. We will see for instance that a new sequence generated
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Spectrum of self-affine measures on the Sierpinski family Monatshefte Math. (IF 0.9) Pub Date : 2024-02-29
Abstract In this study, a spectrum \(\Lambda \) for the integral Sierpinski measures \(\mu _{M, D}\) with the digit set \( D= \left\{ \begin{pmatrix} 0\\ 0 \end{pmatrix}, \begin{pmatrix} 1\\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \end{pmatrix}\right\} \) is derived for a \(2 \times 2\) diagonal matrix M with entries as \(3\ell _1\) and \(3\ell _4\) and for off-diagonal matrix M with both the off-diagonal
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a-Weyl’s theorem and hypercyclicity Monatshefte Math. (IF 0.9) Pub Date : 2024-02-29 Ying Liu, Xiaohong Cao
Let H be a complex infinite dimensional Hilbert space, B(H) be the algebra of all bounded linear operators acting on H, and \(\overline{HC(H)}\) \((\overline{SC(H)})\) be the norm closure of the class of all hypercyclic operators (supercyclic operators) in B(H). An operator \(T\in B(H)\) is said to be with hypercyclicity (supercyclicity) if T is in \(\overline{HC(H)}\) \((\overline{SC(H)})\). Using
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A refinement of the Hille–Wintner comparison theorem and new nonoscillation criteria for half-linear differential equations Monatshefte Math. (IF 0.9) Pub Date : 2024-02-21 Jaroslav Jaroš
A refinement of the Hille–Wintner comparison theorem is obtained for two half-linear differential equations of the second order. As a consequence, some new nonoscillation tests for such equations are derived by means of this improved comparison technique. In most of our results coefficients and their integrals do not need to be nonnegative and are allowed to oscillate in any neighborhood of infinity
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On polynomials in primes, ergodic averages and monothetic groups Monatshefte Math. (IF 0.9) Pub Date : 2024-02-17 Jaroslav Hančl, Radhakrishnan Nair, Jean-Louis Verger-Gaugry
Let G denote a compact monothetic group, and let \(\rho (x) = \alpha _k x^k + \ldots + \alpha _1 x + \alpha _0\), where \(\alpha _0, \ldots , \alpha _k\) are elements of G one of which is a generator of G. Let \((p_n)_{n\ge 1}\) denote the sequence of rational prime numbers. Suppose \(f \in L^{p}(G)\) for \(p> 1\). It is known that if $$\begin{aligned} A_{N}f(x):= {1 \over N} \sum _{n=1}^{N} f(x +
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Pair correlation of real-valued vector sequences Monatshefte Math. (IF 0.9) Pub Date : 2024-02-04 Sneha Chaubey, Shivani Goel
In this article, we investigate the fine-scale statistics of real-valued arithmetic sequences. In particular, we focus on real-valued vector sequences, generalizing previous works of Boca et al. and the first author on the local statistics of integer-valued and rational-valued vector sequences, respectively. As the main results, we prove the Poissonian behavior of the pair correlation function for
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Zero-filter limit issue for the Camassa–Holm equation in Besov spaces Monatshefte Math. (IF 0.9) Pub Date : 2024-02-04 Yuxing Cheng, Jianzhong Lu, Min Li, Xing Wu, Jinlu Li
In this paper, we focus on zero-filter limit problem for the Camassa-Holm equation in the more general Besov spaces. We prove that the solution of the Camassa-Holm equation converges strongly in \(L^\infty (0,T;B^s_{2,r}(\mathbb {R}))\) to the inviscid Burgers equation as the filter parameter \(\alpha \) tends to zero with the given initial data \(u_0\in B^s_{2,r}(\mathbb {R})\). Moreover, we also
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The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech $$^2$$ solutions Monatshefte Math. (IF 0.9) Pub Date : 2024-02-01 Bashar Khorbatly
In the context of the initial data and an amplitude parameter \(\varepsilon \), we establish a local existence result for a highly nonlinear shallow water equation on the real line. This result holds in the space \(H^k\) as long as \(k>5/2\). Additionally, we illustrate that the threshold time for the occurrence of wave breaking in the surging type is on the order of \(\varepsilon ^{-1},\) while plunging
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Aron–Berner extensions of almost Dunford–Pettis multilinear operators Monatshefte Math. (IF 0.9) Pub Date : 2024-01-30 Geraldo Botelho, Luis Alberto Garcia
We study when Aron–Berner extensions of (separately) almost Dunford–Pettis multilinear operators between Banach lattices are (separately) almost Dunford–Pettis. For instance, for a \(\sigma \)-Dedekind complete Banach lattice F containing a copy of \(\ell _\infty \), we characterize the Banach lattices \(E_1, \ldots , E_m\) for which every continuous m-linear operator from \(E_1 \times \cdots \times
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Linear and bilinear Fourier multipliers on Orlicz modulation spaces Monatshefte Math. (IF 0.9) Pub Date : 2024-01-30 Oscar Blasco, Serap Öztop, Rüya Üster
Let \(\Phi _i, \Psi _i\) be Young functions, \(\omega _i\) be weights and \(M^{\Phi _i,\Psi _i}_{\omega _i}(\mathbb {R} ^{d})\) be the corresponding Orlicz modulation spaces for \(i=1,2,3\). We consider linear (respect. bilinear) multipliers on \(\mathbb {R} ^{d}\), that is bounded measurable functions \(m(\xi )\) (respect. \(m(\xi ,\eta )\)) on \(\mathbb {R} ^{d}\) (respect. \(\mathbb {R} ^{2d}\))
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Sharp bounds of nodes for Sturm–Liouville equations Monatshefte Math. (IF 0.9) Pub Date : 2024-01-30
Abstract A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result on sharp bounds of the node for the Sturm–Liouville equation with the Dirichlet boundary condition when the \(L^1\) norm of potentials is given. Based on the outer approximation method, we will reduce this infinite-dimensional optimization problem
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Quadratic Crofton and sets that see themselves as little as possible Monatshefte Math. (IF 0.9) Pub Date : 2024-01-29
Abstract Let \(\Omega \subset \mathbb {R}^2\) and let \(\mathcal {L} \subset \Omega \) be a one-dimensional set with finite length \(L =|\mathcal {L}|\) . We are interested in minimizers of an energy functional that measures the size of a set projected onto itself in all directions: we are thus asking for sets that see themselves as little as possible (suitably interpreted). Obvious minimizers of the
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Existence and regularity results for some nonlinear singular parabolic problems with absorption terms Monatshefte Math. (IF 0.9) Pub Date : 2024-01-27 Mounim El Ouardy, Youssef El Hadfi, Abdelaaziz Sbai
In this paper, we prove the existence of a nonnegative solution to nonlinear parabolic problems with two absorption terms and a singular lower order term. More precisely, we analyze the interaction between the two absorption terms and the singular term to get a solution for the largest possible class of the data. Also, the regularizing effect of absorption terms on the regularity of the solution of
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Existence and stability for a nonlinear model describing arctic gyres Monatshefte Math. (IF 0.9) Pub Date : 2024-01-27 Jin Zhao
This paper is concerned with the bounded solutions for a nonlinear second-order differential equation with asymptotic conditions and boundary condition which arise from the study of Arctic gyres. In the case of Lipschitz continuous nonlinearities, we prove the existence, uniqueness and stability of the bounded solution. An existence result for the general nonlinear vorticity term is also obtained.
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On lattice extensions Monatshefte Math. (IF 0.9) Pub Date : 2024-01-27 Maxwell Forst, Lenny Fukshansky
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Wave-breaking and persistence properties in weighted $$L^p$$ spaces for a Camassa–Holm type equation with quadratic and cubic nonlinearities Monatshefte Math. (IF 0.9) Pub Date : 2024-01-25 Wenguang Cheng, Ji Lin
We consider the Cauchy problem of a Camassa–Holm type equation with quadratic and cubic nonlinearities. We establish a new sufficient condition on the initial data that leads to the wave-breaking for this equation. Moreover, we obtain the persistence results of solutions for the equation in weighted \(L^p\) spaces.
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Groups in which all involutions are 3-transvections Monatshefte Math. (IF 0.9) Pub Date : 2024-01-25 Egle Bettio, Enrico Jabara
Let G be a group which is generated by the set of its involutions, and assume that the set of integers which occur as orders of products of two involutions in G is \(\{1,2,3,4\}\). It is shown that \(G\simeq \textrm{PSL}(2,7)\) or \(G\simeq \textrm{PSU}(3,3)\) or G is a \(\{2,3\}\)-group and \(G/O_{2}(G) \simeq S_{3}\).
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On the deductive strength of the Erdős–Dushnik–Miller theorem and two order-theoretic principles Monatshefte Math. (IF 0.9) Pub Date : 2024-01-24 Eleftherios Tachtsis
We provide answers to open questions from Banerjee and Gopaulsingh (Bull Pol Acad Sci Math 71: 1–21, 2023) about the relationship between the Erdős–Dushnik–Miller theorem (\(\textsf{EDM}\)) and certain weaker forms of the Axiom of Choice (\(\textsf{AC}\)), and we properly strengthen some results from Banerjee and Gopaulsingh (2023). We also settle a part of an open question of Lajos Soukup (stated
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Uniform density topology Monatshefte Math. (IF 0.9) Pub Date : 2024-01-24
Abstract Main results of the paper are: the Lebesgue Density Theorem does not hold for the uniform density points and the uniform density topology is completely regular.
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A sharp two-weight estimate for the maximal operator under a bump condition Monatshefte Math. (IF 0.9) Pub Date : 2024-01-24 Adam Osękowski
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On some special subspaces of a Banach space, from the perspective of best coapproximation Monatshefte Math. (IF 0.9) Pub Date : 2024-01-23
Abstract We study the best coapproximation problem in Banach spaces, by using Birkhoff–James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obtain a necessary condition for the strongly anti-coproximinal subspaces in a reflexive Banach space whose dual space satisfies the Kadets–Klee
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Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit Monatshefte Math. (IF 0.9) Pub Date : 2024-01-22 Jinlu Li, Yanghai Yu, Weipeng Zhu
In this short note, we prove that given initial data \(u_0\in H^s(\mathbb {R})\) with \(s>\frac{3}{2}\) and for some \(T>0\), the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in \(L^\infty (0,T;H^s(\mathbb {R}))\) to the inviscid Burgers equation as the filter parameter \(\alpha \) tends to zero. This is a complement of our recent result on the
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On spectral measures and convergence rates in von Neumann’s Ergodic theorem Monatshefte Math. (IF 0.9) Pub Date : 2024-01-22
Abstract We show that the power-law decay exponents in von Neumann’s Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral measure at the spectral value 1. In this work we also prove that, under an assumption of weak convergence, in the absence of a spectral gap, the convergence rates of the time-average in von Neumann’s Ergodic Theorem depend on sequences of time
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A central limit theorem for integer partitions into small powers Monatshefte Math. (IF 0.9) Pub Date : 2023-12-15 Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy
The study of the well-known partition function p(n) counting the number of solutions to \(n = a_{1} + \dots + a_{\ell }\) with integers \(1 \le a_{1} \le \dots \le a_{\ell }\) has a long history in number theory and combinatorics. In this paper, we study a variant, namely partitions of integers into $$\begin{aligned} n=\left\lfloor a_1^\alpha \right\rfloor +\cdots +\left\lfloor a_\ell ^\alpha \right\rfloor
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Solvability of some integro-differential equations with the double scale anomalous diffusion in higher dimensions Monatshefte Math. (IF 0.9) Pub Date : 2023-12-13 Vitali Vougalter, Vitaly Volpert
The article is devoted to the studies of the existence of solutions of an integro-differential equation in the case of the double scale anomalous diffusion with the sum of the two negative Laplacians raised to two distinct fractional powers in \({\mathbb R}^{d}, \ d=4, 5\). The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for the non-Fredholm elliptic
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Some inequalities for self-mappings of unit ball satisfying the invariant Laplacians Monatshefte Math. (IF 0.9) Pub Date : 2023-11-27 Deguang Zhong, Meilan Huang, Dongping Wei
In this paper, we study those mappings in unit ball satisfying the Dirichlet problem of the following differential operators $$\begin{aligned} \Delta _{\gamma }=\big (1-|x|^{2}\big )\cdot \left[ \frac{1-|x|^{2}}{4}\cdot \sum _{i}\frac{\partial ^{2}}{\partial x_{i}^{2}}+\gamma \sum _{i}x_{i}\cdot \frac{\partial }{\partial x_{i}}+\gamma \left( \frac{n}{2}-1-\gamma \right) \right] . \end{aligned}$$ Our
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Strong tree properties, Kurepa trees, and guessing models Monatshefte Math. (IF 0.9) Pub Date : 2023-11-25 Chris Lambie-Hanson, Šárka Stejskalová
We investigate the generalized tree properties and guessing model properties introduced by Weiß and Viale, as well as natural weakenings thereof, studying the relationships among these properties and between these properties and other prominent combinatorial principles. We introduce a weakening of Viale and Weiß’s Guessing Model Property, which we call the Almost Guessing Property, and prove that it
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Cohomology of quasi-abelianized braid groups Monatshefte Math. (IF 0.9) Pub Date : 2023-11-24 Filippo Callegaro, Ivan Marin
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Infinite products involving the period-doubling sequence Monatshefte Math. (IF 0.9) Pub Date : 2023-11-24 John M. Campbell
We explore the evaluation of infinite products involving the automatic sequence \((d_{n}: n \in \mathbb {N}_{0})\) known as the period-doubling sequence, inspired by the work of Allouche, Riasat, and Shallit on the evaluation of infinite products involving the Thue–Morse or Golay–Shapiro sequences. Our methods allow for the application of integral operators that result in new product expansions for
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A short note on coproducts of Abelian pro-Lie groups Monatshefte Math. (IF 0.9) Pub Date : 2023-11-19 Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo
The notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct.
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A Voronoi summation formula for non-holomorphic Maass forms of half-integral weight Monatshefte Math. (IF 0.9) Pub Date : 2023-11-18 Olga Balkanova, Dmitry Frolenkov
We prove a Voronoi summation formula for non-holomorphic half-integral weight Maass forms on \(\Gamma _0(4)\) without any restrictions on the denominator of a fraction in the exponential function. As an application we obtain a Voronoi summation formula for the values of Zagier L-series.
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An extension of Aigner’s theorem Monatshefte Math. (IF 0.9) Pub Date : 2023-11-18 Nguyen Xuan Tho
In 1957, Aigner (Monatsh Math 61:147–150, 1957) showed that the equations \(x^6+y^6=z^6\) and \(x^9+y^9=z^9\) have no solutions in any quadratic number field with \(xyz\ne 0\). We show that Aigner’s result holds for all equations \(x^{3n}+y^{3n}=z^{3n}\), where \(n\ge 2\) is a positive integer. The proof combines Aigner’s idea with deep results on Fermat’s equation and its variants.
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Eigenvalues of truncated unitary matrices: disk counting statistics Monatshefte Math. (IF 0.9) Pub Date : 2023-11-16 Yacin Ameur, Christophe Charlier, Philippe Moreillon
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Maximal run-length function with constraints: a generalization of the Erdős–Rényi limit theorem and the exceptional sets Monatshefte Math. (IF 0.9) Pub Date : 2023-11-13 Yu-Feng Wu
Let \({\textbf{A}}=\{A_i\}_{i=1}^{\infty }\) be a sequence of sets with each \(A_i\) being a non-empty collection of 0-1 sequences of length i. For \(x\in [0,1)\), the maximal run-length function \(\ell _n(x,{\textbf{A}})\) (with respect to \({\textbf{A}}\)) is defined to be the largest k such that in the first n digits of the dyadic expansion of x there is a consecutive subsequence in \(A_k\). Suppose
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An existence and uniqueness result about algebras of Schwartz distributions Monatshefte Math. (IF 0.9) Pub Date : 2023-11-04 Nuno Costa Dias, Cristina Jorge, João Nuno Prata
We prove that there exists essentially one minimal differential algebra of distributions \(\mathcal A\), satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l’impossibilité de la multiplication des distributions, 1954], and such that \(\mathcal C_p^{\infty } \subseteq \mathcal A\subseteq \mathcal D' \) (where \(\mathcal C_p^{\infty }\) is the set of piecewise
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Comparison of symbolic and ordinary powers of parity binomial edge ideals Monatshefte Math. (IF 0.9) Pub Date : 2023-11-02 Nadia Taghipour, Shamila Bayati, Farhad Rahmati
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The geometry of discrete asymptotic-geodesic 4-webs in isotropic 3-space Monatshefte Math. (IF 0.9) Pub Date : 2023-11-03 Christian Müller, Helmut Pottmann
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A two plus one dimensional continuous wavelet transform Monatshefte Math. (IF 0.9) Pub Date : 2023-11-03 Raja Milad, Keith F. Taylor
The group \(G_2\) of invertible affine transformations of \({\mathbb {R}}^2\) has, up to equivalence, one irreducible representation that is square–integrable. Two new realizations of this representation are presented and the associated Duflo–Moore operator is calculated. Two novel, but equivalent, continuous wavelet transforms, acting on functions of two plus one variables, are then derived.
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Difference of irrationality measure functions Monatshefte Math. (IF 0.9) Pub Date : 2023-11-04 Viktoria Rudykh, Nikita Shulga
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Extendibility and boundedness of invariants on singularities of wavefronts Monatshefte Math. (IF 0.9) Pub Date : 2023-11-01 T. A. Medina-Tejeda
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Oscillation criterion for linear equations with coefficients containing powers of natural logarithm Monatshefte Math. (IF 0.9) Pub Date : 2023-10-13 Petr Hasil, Michal Pospíšil, Jiřina Šišoláková, Michal Veselý
Applying an averaging technique for the adapted Prüfer angle, we obtain an oscillation criterion for linear second order differential equations whose coefficients consist of products of powers of natural logarithm and general (bounded or unbounded) continuous functions. The presented criterion is illustrated by new corollaries and examples. The novelty is caused by the used averaging technique over
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Discrete series of odd general spin groups Monatshefte Math. (IF 0.9) Pub Date : 2023-10-05 Yeansu Kim, Ivan Matić
We obtain a Mœglin–Tadić type classification of the non-cuspidal discrete series of odd general spin groups over non-archimedean local fields of characteristic zero. Our approach presents a simplified, uniform, and slightly different construction of a bijective correspondence between the set of isomorphism classes of non-cuspidal discrete series representations and the set of so called admissible triples
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Potency in soluble groups Monatshefte Math. (IF 0.9) Pub Date : 2023-10-04 B. A. F. Wehrfritz
We prove in particular that if G is a soluble group with no non-trivial locally finite normal subgroups, then G is p-potent for every prime p for which G has no Prüfer p-sections. (A group G is p-potent if for every power n of p and for any element x of G of infinite order or of finite order divisible by n there is a normal subgroup N of G of finite index such that the order of x modulo N is n. A Prüfer
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$$C^{*}$$ -algebra structure on vector valued-Banach algebras Monatshefte Math. (IF 0.9) Pub Date : 2023-10-03 Mitra Amiri, Ali Rejali
Let \( {\mathcal {A}}\) be a commutative semisimple Banach algebra, X be a locally compact Hausdorff topological space and G be a locally compact topological group. In this paper, we investigate several properties of vector valued Banach algebras \( C_0(X , {\mathcal {A}})\), \( L^p(G,{\mathcal {A}})\), \(\ell ^p (X , {\mathcal {A}})\) and \( \ell ^{\infty }(X , {\mathcal {A}})\). We prove that these
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New examples of compact Weyl-parallel manifolds Monatshefte Math. (IF 0.9) Pub Date : 2023-09-27 Andrzej Derdzinski, Ivo Terek
We prove the existence of compact pseudo-Riemannian manifolds with parallel Weyl tensor which are neither conformally flat nor locally symmetric, and represent all indefinite metric signatures in all dimensions \(\,n\ge 5\). Until now such manifolds were only known to exist in dimensions \(\,n=3j+2\), where j is any positive integer; see Derdzinski and Roter (Ann Global Anal Geom 37(1):73–90, 2010
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Equivariant basic cohomology of singular Riemannian foliations Monatshefte Math. (IF 0.9) Pub Date : 2023-09-28 Francisco C. Caramello
We extend the notion of equivariant basic cohomology to singular Riemannian foliations with transverse infinitesimal actions, aiming the particular case of singular Killing foliations, which admit a natural transverse action describing the closures of the leaves. This class of foliations includes those coming from isometric actions, as well as orbit-like foliations on simply connected manifolds. This
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Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings Monatshefte Math. (IF 0.9) Pub Date : 2023-09-26 Manzi Huang, Zhihao Xu
In this paper, we study the existence of traces for Sobolev spaces on the hyperbolic filling X of a compact metric space Z equipped with a doubling measure. Given a suitable metric on X, we can regard Z as the boundary of X. After equipping X with a weighted measure \(\mu _\rho \) via the measure on Z and the Euclidean arc length, we give characterizations for the existence of traces for first-order
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Decomposability and local spectral properties of a normal linear relation Monatshefte Math. (IF 0.9) Pub Date : 2023-09-26 Yosra Barkaoui, Maher Mnif
Our objective in this paper is to show that, similarly to the case of normal operators, a normal linear relation on a Hilbert space H satisfies several notions related to the local spectral theory such as the single valued extension property (SVEP), Bishop and Dunford properties, and more generally the spectral decomposability. To that end, we shall start by introducing all those notions for a closed
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Estimates for $$\delta $$ -periodic eigenvalues of two-component Novikov system Monatshefte Math. (IF 0.9) Pub Date : 2023-09-26 Xun Wang, Nana Xie
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Ratios conjecture for quadratic Hecke L-functions in the Gaussian field Monatshefte Math. (IF 0.9) Pub Date : 2023-09-27 Peng Gao, Liangyi Zhao
We develop the L-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke L-functions in the Gaussian field using multiple Dirichlet series under the generalized Riemann hypothesis. We also obtain an asymptotical formula for the first moment of central values of the same family of L-functions, obtaining an error term of size \(
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An application of the theory of viscosity solutions to higher order differential equations Monatshefte Math. (IF 0.9) Pub Date : 2023-09-25 Matei P. Coiculescu
We directly apply the theory of viscosity solutions to partial differential equations of order greater than two. We prove that there exists a solution in \(C^{2,\alpha }(B_R)\cap C(\overline{B_R})\) for the inhomogeneous \(\infty \)-Bilaplacian equation on a ball \(B_R\subset {\mathbb {R}}^n\): $$\begin{aligned} \Delta _\infty ^2 u:=(\Delta u)^3 {|D(\Delta u)|}^2 =f(x) \end{aligned}$$ with Navier Boundary
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Orbital stability of periodic peakons for the higher-order modified Camassa–Holm equation Monatshefte Math. (IF 0.9) Pub Date : 2023-09-26 Gezi Chong, Ying Fu, Hao Wang
Considered herein is the orbital stability of the periodic peaked solitons for the higher-order modified Camassa–Holm equation. This equation can be viewed as a natural higher-order generalization of the modified Camassa–Holm equation, and admits a single peaked soliton and multi-peakons. We first show that the equation possesses the periodic peakons. Furthermore, it is proved that the periodic peakons
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Estimates on Bloch constants for certain log-p-harmonic mappings Monatshefte Math. (IF 0.9) Pub Date : 2023-09-26 Ming-Sheng Liu, Xin Wang, Kit Ian Kou
In this paper, we first provide a brief overview of Landau-type theorems for log-p-harmonic mappings. Next, we establish four new versions of Landau-type theorems for certain bounded p-harmonic mappings F with \(J_F(0)=1\). Then, as applications of these results, the corresponding Landau-type theorems for certain log-p-harmonic mappings f with \(J_f(0)=1\) are provided. In particular, several sharp
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The symmetry of steady stratified periodic gravity water waves Monatshefte Math. (IF 0.9) Pub Date : 2023-09-25 Fei Xu, Fengquan Li, Yong Zhang
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Existence, regularity and symmetry of periodic traveling waves for Gardner–Ostrovsky type equations Monatshefte Math. (IF 0.9) Pub Date : 2023-09-07 Gabriele Bruell, Long Pei
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Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations Monatshefte Math. (IF 0.9) Pub Date : 2023-09-04 Victor Fadinger-Held, Sophie Frisch, Daniel Windisch
Let V be a valuation ring of a global field K. We show that for all positive integers k and \(1 < n_1 \le \cdots \le n_k\) there exists an integer-valued polynomial on V, that is, an element of \({{\,\textrm{Int}\,}}(V) = \{ f \in K[X] \mid f(V) \subseteq V \}\), which has precisely k essentially different factorizations into irreducible elements of \({{\,\textrm{Int}\,}}(V)\) whose lengths are exactly
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Gessel–Lucas congruences for sporadic sequences Monatshefte Math. (IF 0.9) Pub Date : 2023-08-31 Armin Straub
For each of the 15 known sporadic Apéry-like sequences, we prove congruences modulo \({\varvec{p^2}}\) that are natural extensions of the Lucas congruences modulo p. This extends a result of Gessel for the numbers used by Apéry in his proof of the irrationality of \({\varvec{\zeta (3)}}\). Moreover, we show that each of these sequences satisfies two-term supercongruences modulo \({\varvec{p^{2r}}}\)
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On the well-posedness of dispersive–dissipative one dimensional equations with non decaying initial data Monatshefte Math. (IF 0.9) Pub Date : 2023-08-29 May Abdallah
In this paper, we study the well-posedness of the Cauchy problem for a dissipative version of dispersive one dimensional equations of Korteweg de Vries type without any assumption on the decay of its initial data. We consider purely dispersion operators between BO and KdV combined with purely dissipation operators. We show in particular the local well-posedness of our equations in Zhidkov spaces \(Z^s\)