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Two-dimensional Weyl sums failing square-root cancellation along lines Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Julia Brandes, Igor E. Shparlinski
We show that a certain two-dimensional family of Weyl sums of length $P$ takes values as large as $P^{3/4+o(1)}$ on almost all linear slices of the unit torus, contradicting a widely held expectation that Weyl sums should exhibit square-root cancellation on generic subvarieties of the unit torus. This is an extension of a result of J. Brandes, S. T. Parsell, C. Poulias, G. Shakan and R. C. Vaughan
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Overcompleteness of coherent frames for unimodular amenable groups Ark. Mat. (IF 0.7) Pub Date : 2023-11-13
This paper concerns the overcompleteness of coherent frames for unimodular amenable groups. It is shown that for coherent frames associated with a localized vector a set of positive Beurling density can be removed yet still leave a frame. The obtained results extend various theorems of $\href{http://www.ams.org/mathscinet-getitem?mr=2235170}{[\textrm{J. Fourier Anal. Appl., 12(3):307-344, 2006}]}$
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Quantum Euler class and virtual Tevelev degrees of Fano complete intersections Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Alessio Cela
We compute the quantum Euler class of Fano complete intersections $X$ in a projective space. In particular, we prove a recent conjecture of A. Buch and R. Pandharipande, namely [$\href{https://arxiv.org/abs/2112.14824}{7}$, Conjecture 5.14]. Finally we apply our result to obtain formulas for the virtual Tevelev degrees of $X$. An algorithm computing all genus $0$ two-point Hyperplane Gromov–Witten
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The extensions of $t$-structures Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Xiao-Wu Chen, Zengqiang Lin, Yu Zhou
We reformulate a result of Bernhard Keller on extensions of $t$-structures and give a detailed proof. In the study of hereditary $t$-structures, the notions of regular $t$-structures and global dimensions arise naturally.
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The spectral picture of Bergman–Toeplitz operators with harmonic polynomial symbols Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Kunyu Guo, Xianfeng Zhao, Dechao Zheng
This paper shows some new phenomenon in the spectral theory of Toeplitz operators on the Bergman space, which is considerably different from that of Toeplitz operators on the Hardy space. On the one hand, we prove that the spectrum of the Toeplitz operator with symbol $\overline{z}+p$ is always connected for every polynomial $p$ with degree less than $3$. On the other hand, we show that for each integer
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A Poisson basis theorem for symmetric algebras of infinite-dimensional Lie algebras Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Omar León Sánchez, Susan J. Sierra
We consider when the symmetric algebra of an infinite-dimensional Lie algebra, equipped with the natural Poisson bracket, satisfies the ascending chain condition (ACC) on Poisson ideals. We define a combinatorial condition on a graded Lie algebra which we call Dicksonian because it is related to Dickson’s lemma on finite subsets of $\mathbb{N}^k$. Our main result is: Theorem. If $\mathfrak{g}$ is a
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Minimal-mass blow-up solutions for inhomogeneous nonlinear Schrödinger equations with growing potentials Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Naoki Matsui
In this paper, we consider the following equation:\[i \frac{\partial u}{\partial t} + \Delta u + g(x) {\lvert u \rvert}^{4/N} u - Wu = 0 \textrm{.}\]We construct a critical-mass solution that blows up at a finite time and describe the behaviour of the solution in the neighbourhood of the blow-up time. Banica–Carles–Duyckaerts (2011) have shown the existence of a critical-mass blow-up solution under
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On the sum of a prime power and a power in short intervals Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Yuta Suzuki
Let $R_{k,\ell} (N)$ be the representation function for the sum of the $k$‑th power of a prime and the $\ell$‑th power of a positive integer. Languasco and Zaccagnini (2017) proved an asymptotic formula for the average of $R_{1,2} (N)$ over short intervals $(X, X+H]$ of the length $H$ slightly shorter than $X^{\frac{1}{2}}$, which is shorter than the length $X^{\frac{1}{2}+\varepsilon}$ in the exceptional
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Hilbert schemes of points on smooth projective surfaces and generalized Kummer varieties with finite group actions Ark. Mat. (IF 0.7) Pub Date : 2023-11-13 Sailun Zhan
Göttsche and Soergel gave formulas for the Hodge numbers of Hilbert schemes of points on a smooth algebraic surface and the Hodge numbers of generalized Kummer varieties. When a smooth projective surface $S$ admits an action by a finite group $G$, we describe the action of $G$ on the Hodge pieces via point counting. Each element of $G$ gives a trace on $\sum^\infty_{n=0} \sum^\infty_{i=0} (-1)^i H^i
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Yagita’s counter-examples and beyond Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Sanghoon Baek, Nikita A. Karpenko
A conjecture on a relationship between the Chow and Grothendieck rings for the generically twisted variety of Borel subgroups in a split semisimple group $G$, stated by the second author, has been disproved by Nobuaki Yagita in characteristic $0$ for $G=\operatorname{Spin}(2n+1)$ with $n=8$ and $n=9$. For $n=8$, the second author provided an alternative simpler proof of Yagita’s result, working in
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Universality of general Dirichlet series with respect to translations and rearrangements Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Frédéric Bayart
We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.
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Explosive growth for a constrained Hastings–Levitov aggregation model Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Nathanaël Berestycki, Vittoria Silvestri
We consider a constrained version of the $\operatorname{HL}(0)$ Hastings–Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this gives rise to a non-trivial limiting shape, we prove that the cluster grows explosively: in the upper half plane, the aggregate accumulates infinite diameter
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Removability of product sets for Sobolev functions in the plane Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Ugo Bindini, Tapio Rajala
We study conditions on closed sets $C, F \subset \mathbb{R}$ making the product $C \times F$ removable or non-removable for $W^{1,p}$. The main results show that the Hausdorff-dimension of the smaller dimensional component $C$ determines a critical exponent above which the product is removable for some positive measure sets $F$, but below which the product is not removable for another collection of
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A complex-analytic approach to streamline properties of deep-water Stokes waves Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Olivia Constantin
Using methods from complex analysis we obtain some qualitative results for certain streamline characteristics in a deep-water Stokes flow.
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Regularity of symbolic powers of square-free monomial ideals Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Thi Hien Truong, Nam Trung Tran
We study the regularity of symbolic powers of square-free monomial ideals. We prove that if $I = I_\Delta$ is the Stanley–Reisner ideal of a simplicial complex $\Delta$, then $\operatorname{reg}(I^{(n)}) \leqslant \delta (n-1)+b$ for all $n \geqslant 1$, where $\delta = \operatorname{lim}_{n \to \infty} \operatorname{reg}(I^{(n)}) / n$, $b=\max \lbrace \operatorname{reg}(I_\Gamma ) \vert \Gamma$ is
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A Whittaker category for the symplectic Lie algebra and differential operators Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Yang Li, Jun Zhao, Yuanyuan Zhang, Genqiang Liu
For any $n \in \mathbb{Z}_{\geq 2}$, let $\mathfrak{m}_n$ be the subalgebra of $\mathfrak{sp}_{2n}$ spanned by all long negative root vectors $X_{-2 \varepsilon_i} , i=1, \dotsc , n$. Then ($\mathfrak{sp}_{2n}$, $\mathfrak{m}_n$) is a Whittaker pair in the sense of a definition given by Batra and Mazorchuk. In this paper, we use differential operators to study the category of $\mathfrak{sp}_{2n}$-modules
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Estimates of $p$-harmonic functions in planar sectors Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Niklas L. P. Lundström, Jesper Singh
Suppose that $p \in (1,\infty], \nu \in [1/2,\infty), {S_{\nu }}=\left\{({x_{1}},{x_{2}})\in {\mathbb{R}^{2}}\setminus \{(0,0)\}:|\phi | \lt \frac{\pi }{2\nu }\right\}$, where $\phi$ is the polar angle of $(x_1, x_2)$. Let $R \gt 0$ and $\omega_p (x)$ be the $p$-harmonic measure of $\partial B(0,R) \cap \mathcal{S}_\nu$ at $x$ with respect to $B(0,R) \cap S_\nu$. We prove that there exists a constant
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Perturbations of embedded eigenvalues for self-adjoint ODE systems Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Sara Maad Sasane, Alexia Papalazarou
We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in $L^2 (\mathbb{R} ; \mathbb{R}^n)$. In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension
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On local and semi-matching colorings of split graphs Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Yaroslav Shitov
A semi-matching coloring of a finite simple graph $G=(V,E)$ is a mapping $\varphi$ from $V$ to $\lbrace 1,\dotsc,k \rbrace$ such that (i) every color class is an independent set, and (ii) the edge set of the graph induced by the union of any two consecutive color classes is a matching. A semi-matching coloring $\varphi$ is a local coloring if, in addition, (iii) the union of any three consecutive color
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Intersection theory and Chern classes in Bott–Chern cohomology Ark. Mat. (IF 0.7) Pub Date : 2023-04-26 Xiaojun Wu
In this article, we study the axiomatic approach of Grivaux in [Gri10] for rational Bott–Chern cohomology, and use it in particular to define Chern classes of coherent sheaves in rational Bott–Chern cohomology. This method also allows us to derive a Riemann–Roch–Grothendieck formula for a projective morphism between smooth complex compact manifolds.
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On the double of the Jordan plane Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 Nicolás Andruskiewitsch, François Dumas, Héctor Martín Peña Pollastri
We compute the simple finite-dimensional modules and the center of the Drinfeld double of the Jordan plane introduced in [Andruskiewitsch, N. and Peña Pollastri, H. M., “On the restricted Jordan plane in odd characteristic”, J. Algebra Appl. 20, 2140012 (2021). MR4209966] assuming that the characteristic is zero.
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Notes on $H^{\log}$: structural properties, dyadic variants, and bilinear $H^1$-$\operatorname{BMO}$ mappings Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 Odysseas Bakas, Sandra Pott, Salvador Rodríguez-López, Alan Sola
This article is devoted to a study of the Hardy space $H^{\log} (\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space $H^1$ and a function in $BMO$ to distributions that belong to $H^{\log}$ based on dyadic paraproducts. We also point out analogues of classical results of Hardy–Littlewood
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Faces of polyhedra associated with relation modules Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 Germán Benitez, Luis Enrique Ramirez
Relation Gelfand–Tsetlin $\mathfrak{gl}_n$-modules were introduced in [FRZ19], and are determined by some special directed graphs and Gelfand–Tsetlin characters. In this work, we constructed polyhedra associated with the class of relation modules, which includes as a particular case, any classical Gelfand–Tsetlin polytope. Following the ideas presented in [LM04], we give a characterization of $d$-faces
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Weil–Poincaré series and topology of collections of valuations on rational double points Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 A. Campillo, F. Delgado, S.M. Gusein-Zade
Earlier it was described to which extent the Alexander polynomial in several variables of an algebraic link in the Poincaré sphere determines the topology of the link. It was shown that, except some explicitly described cases, the Alexander polynomial of an algebraic link determines the combinatorial type of the minimal resolution of the curve and therefore the topology of the corresponding link. The
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Proper holomorphic embeddings of complements of large Cantor sets in $\mathbb{C}^2$ Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 G.D. Di Salvo, E.F. Wold
We prove that there exist Cantor sets of arbitrarily large $2$-dimensional Lebesgue measure whose complements admit proper holomorphic embeddings in $\mathbb{C}^2$.
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Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 F. Forstnerič
In this paper, we construct open Stein neighbourhoods of compact sets of the form $A \cup K$ in a complex space, where $K$ is a compact holomorphically convex set, $A$ is a compact complex curve with boundary $bA$ of class $\mathscr{C}^2$ which may intersect $K$, and the set $A \cap K$ is $\mathscr{O}(A)$-convex.
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On Hedenmalm–Shimorin type inequalities Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 Yong Han, Yanqi Qiu, Zipeng Wang
We present a direct proof of an Hedenmalm–Shimorin inequality for short antidiagonals proved recently in [HS20, Advances in Mathematics, 2020] and give the three tensor analogue of such inequality.
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On the existence of Auslander–Reiten $n$-exangles in $n$-exangulated categories Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 Jian He, Jiangsheng Hu, Dongdong Zhang, Panyue Zhou
Let $\mathscr{C}$ be an $n$-exangulated category. In this note, we show that if $\mathscr{C}$ is locally finite, then $\mathscr{C}$ has Auslander–Reiten $n$-exangles. This unifies and extends results of Xiao–Zhu, Zhu–Zhuang, Zhou, and Xie–Lu–Wang for triangulated, extriangulated, $(n+2)$-angulated and $n$-abelian categories, respectively.
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Dimension compression and expansion under homeomorphisms with exponentially integrable distortion Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 Lauri Hitruhin
We improve both dimension compression and expansion bounds for homeomorphisms with $p$-exponentially integrable distortion. To the first direction, we also introduce estimates for the compression multifractal spectra, which will be used to estimate compression of dimension, and for the rotational multifractal spectra. For establishing the expansion case, we use the multifractal spectra of the inverse
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Beurling’s theorem on the Heisenberg group Ark. Mat. (IF 0.7) Pub Date : 2022-10-26 Sundaram Thangavelu
We formulate and prove an analogue of Beurling’s theorem for the Fourier transform on the Heisenberg group. As a consequence, we deduce Hardy and Cowling–Price theorems.
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Multiple solutions for two classes of quasilinear problems defined on a nonreflexive Orlicz–Sobolev space Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Claudianor O. Alves, Sabri Bahrouni, Marcos L. M. Carvalho
In this paper we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz–Sobolev space. Here, we use the variational methods developed by Szulkin [34] combined with some properties of the weak* topology.
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Hamiltonian Carleman approximation and the density property for coadjoint orbits Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Fusheng Deng, Erlend Fornæss Wold
For a complex Lie group $G$ with a real form $G_0 \subset G$, we prove that any Hamiltonian automorphism $\phi$ of a coadjoint orbit $\mathcal{O}_0$ of $G_0$ whose connected components are simply connected, may be approximated by holomorphic $\mathcal{O}_0$-invariant symplectic automorphism of the corresponding coadjoint orbit of $G$ in the sense of Carleman, provided that $\mathcal{O}$ is closed.
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Fundamental solutions of generalized non-local Schrodinger operators Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Duc Do Tan
Let $d \in {\lbrace 1, 2, 3, \dotsc \rbrace}$ and $s \in (0, 1)$ be such that $d \gt 2s$. We consider a generalized non-local Schrodinger operator of the form\[L=L_K + \nu \; \textrm{,}\]where $L_K$ is a non-local operator with kernel $K$ that includes the fractional Laplacian $(-\Delta)^s$ for $s \in (0, 1)$ as a special case. The potential $\nu$ is a doubling measure subjected to a certain constraint
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On the arithmetic of monoids of ideals Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Alfred Geroldinger, M. Azeem Khadam
We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of $r$-invertible $r$-ideals for certain ideal systems $r$) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero ideals of polynomial rings with at least two indeterminates over noetherian domains. Among others, we show that they are not transfer Krull but they share several
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Duality for Witt-divisorial sheaves Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Niklas Lemcke
We adapt ideas from Ekedahl [Eke84] to prove a Serre-type duality for Witt-divisorial sheaves of $\mathbb{Q}$‑Cartier divisors on a smooth projective variety over a perfect field of finite characteristic. We also explain its relationship to Tanaka’s vanishing theorems [Tan20].
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Extension of the $2$-representation theory of finitary $2$-categories to locally (graded) finitary $2$-categories Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 James Macpherson
We extend the $2$-representation theory of finitary $2$-categories to certain $2$-categories with infinitely many objects, called locally finitary $2$-categories, and extend the classical classification results of simple transitive $2$-representations of weakly fiat $2$-categories to this environment. We also consider locally finitary $2$-categories and $2$-representations with a grading, and prove
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On a remark by Ohsawa related to the Berndtsson–Lempert method for $L^2$-holomorphic extension Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Tai Terje Huu Nguyen, Xu Wang
In [15, Remark 4.1], Ohsawa asked whether it is possible to prove Theorem 4.1 and Theorem 0.1 in [15] using the Berndtsson–Lempert method. We shall answer Ohsawa’s question affirmatively in this paper. Our approach also suggests to introduce the Legendre–Fenchel theory and weak psh‑geodesics into the Berndtsson–Lempert method.
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Remarks on random walks on graphs and the Floyd boundary Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Panagiotis Spanos
We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, $p^{(n)} (v,w) \leq C \rho^n$, where $\rho \lt 1$ is the spectral radius, then for any Floyd function $f$ that satisfies $\sum^{\infty}_{n=1} nf(n) \lt \infty$, the Dirichlet problem
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A quantitative Gauss–Lucas theorem Ark. Mat. (IF 0.7) Pub Date : 2022-05-16 Vilmos Totik
A conjecture of T. Richards is proven which yields a quantitative version of the classical Gauss–Lucas theorem: if $K$ is a convex set, then for every $\varepsilon \gt 0$ there is an $\alpha_{\varepsilon} \lt 1$ such that if a polynomial $P_n$ of degree at most $n$ has $k \geq \alpha_{\varepsilon} n$ zeros in $K$, then $P^{\prime}_n$ has at least $k-1$ zeros in the $\varepsilon$-neighborhood of $K$
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Promotion and cyclic sieving on families of SSYT Ark. Mat. (IF 0.7) Pub Date : 2021-11-11 Per Alexandersson, Ezgi Kantarci Oğuz, Svante Linusson
We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as CSP-polynomial. The second family contains skew shapes, consisting of disjoint rectangles. Again, the charge generating polynomial together with promotion exhibits
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Multiplication in Sobolev spaces, revisited Ark. Mat. (IF 0.7) Pub Date : 2021-11-11 A. Behzadan, M. Holst
In this article, we re-examine some of the classical pointwise multiplication theorems in Sobolev–Slobodeckij spaces, in part motivated by a simple counter-example that illustrates how certain multiplication theorems fail in Sobolev–Slobodeckij spaces when a bounded domain is replaced by $\mathbb{R}^n$. We identify the source of the failure, and examine why the same failure is not encountered in Bessel
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Pull-back of singular Levi-flat hypersurfaces Ark. Mat. (IF 0.7) Pub Date : 2021-11-11 Andrés Beltrán, Arturo Fernández-Pérez, Hernán Neciosup
We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat hypersurface in a complex projective surface under a rational map or to be the pull-back of a real algebraic curve under a meromorphic function. In particular, we
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On families between the Hardy–Littlewood and spherical maximal functions Ark. Mat. (IF 0.7) Pub Date : 2021-11-11 Georgios Dosidis, Loukas Grafakos
We study a family of maximal operators that provides a continuous link connecting the Hardy–Littlewood maximal function to the spherical maximal function. Our theorems are proved in the multilinear setting but may contain new results even in the linear case. For this family of operators we obtain bounds between Lebesgue spaces in the optimal range of exponents.
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The local image problem for complex analytic maps Ark. Mat. (IF 0.7) Pub Date : 2021-11-11 Cezar Joiţa, Mihai Tibăr
We address the question “when the local image of a map is well defined” and answer it in case of holomorphic map germs with target $(\mathbb{C}^2, 0)$. We prove a criterion for holomorphic map germs $(X, x) \to (Y, y)$ to be locally open, solving a conjecture by Huckleberry in all dimensions.
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A Riemann–Roch type theorem for twisted fibrations of moment graphs Ark. Mat. (IF 0.7) Pub Date : 2021-11-11 Martina Lanini, Kirill Zainoulline
In the present paper we extend the Riemann–Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and push-forwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann–Roch theorem for moment graphs. As an application, we obtain the Riemann–Roch type theorem for the equivariant $K$‑theory of some Kac–Moody flag varieties.
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Resonances over a potential well in an island Ark. Mat. (IF 0.7) Pub Date : 2021-11-11 Johannes Sjöstrand, Maher Zerzeri
In this paper we study the distribution of scattering resonances for a multi-dimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.
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Local and $2$-local automorphisms of simple generalized Witt algebras Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Yang Chen, Kaiming Zhao, Yueqiang Zhao
In this paper, we prove that every invertible $2$-local or local automorphism of a simple generalized Witt algebra over any field of characteristic $0$ is an automorphism. Furthermore, every $2$-local or local automorphism of Witt algebras $W_n$ is an automorphism for all $n \in \mathbb{N}$. But some simple generalized Witt algebras indeed have $2$-local (and local) automorphisms that are not automorphisms
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Optimal unions of scaled copies of domains and Pólya's conjecture Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Pedro Freitas, Jean Lagacé, Jordan Payette
Given a bounded Euclidean domain $\Omega$, we consider the sequence of optimisers of the $k$th Laplacian eigenvalue within the family consisting of all possible disjoint unions of scaled copies of $\Omega$ with fixed total volume. We show that this sequence encodes information yielding conditions for $\Omega$ to satisfy Pólya’s conjecture with either Dirichlet or Neumann boundary conditions. This is
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Exponential localization in 2D pure magnetic wells Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Y. Guedes Bonthonneau, N. Raymond, S. Vũ Ngọc
We establish a magnetic Agmon estimate in the case of a purely magnetic single non-degenerate well, by means of the Fourier–Bros–Iagolnitzer transform and microlocal exponential estimates à la Martinez–Sjöstrand.
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A.s. convergence for infinite colour Pólya urns associated with random walks Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Svante Janson
We consider Pólya urns with infinitely many colours that are of a random walk type, in two related versions. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on the offset distribution. This improves results by Bandyopadhyay and Thacker (2014–2017; convergence in probability), and Mailler and Marckert (2017; a.s. convergence
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Metric Lie groups admitting dilations Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Enrico Le Donne, Sebastiano Nicolussi Golo
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0,\infty) \to \operatorname{Aut}(G), \lambda \mapsto \delta_\lambda$, so that $d (\delta_\lambda x, \delta_\lambda y) = \lambda d(x, y),$ for all $x,y \in G$ and all $\lambda \gt 0$. First, we show that all such distances are admissible, that is
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On the tree structure of orderings and valuations on rings Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Simon Müller
Let $R$ be a not necessarily commutative ring with $1$. In the present paper we first introduce a notion of quasi-orderings, which axiomatically subsumes all the orderings and valuations on $R$. We proceed by uniformly defining a coarsening relation $\leq$ on the set $\mathcal{Q}(R)$ of all quasi-orderings on $R$. One of our main results states that $(\mathcal{Q}(R), \leq^\prime)$ is a rooted tree
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A recursive formula for osculating curves Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Giosuè Muratore
Let $X$ be a smooth complex projective variety. Using a construction devised by Gathmann, we present a recursive formula for some of the Gromov–Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X$. This generalizes the classical well known pairs of inflection (asymptotic) lines
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Exponential mixing property for automorphisms of compact Kähler manifolds Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Hao Wu
Let $f$ be a holomorphic automorphism of a compact Kähler manifold. Assume that $f$ admits a unique maximal dynamic degree $d_p$ with only one eigenvalue of maximal modulus. Let $\mu$ be its equilibrium measure. In this paper, we prove that $\mu$ is exponentially mixing for all d.s.h. test functions.
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On the existence of curves with prescribed $a$-number Ark. Mat. (IF 0.7) Pub Date : 2021-04-01 Zijian Zhou
We study the existence of Artin–Schreier curves with large $a$‑number. We show that Artin–Schreier curves with large $a$‑number can be written in certain forms and discuss their supersingularity. We also give a basis of the de Rham cohomology of Artin–Schreier curves. By computing the rank of the Hasse–Witt matrix of the curve, we also give bounds on the $a$‑number of trigonal curves of genus $5$ in
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Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations Ark. Mat. (IF 0.7) Pub Date : 2020-10-01 Giuseppe della Sala, Bernhard Lamel, Michael Reiter
In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we show higher order infinitesimal conditions can be used to give a characterization of local rigidity.
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The doubling metric and doubling measures Ark. Mat. (IF 0.7) Pub Date : 2020-10-01 János Flesch, Arkadi Predtetchinski, Ville Suomala
We introduce the so-called doubling metric on the collection of non-empty bounded open subsets of a metric space. Given an open subset $\mathbb{U}$ of a metric space $X$, the predecessor $\mathbb{U}_\ast$ of $\mathbb{U}$ is defined by doubling the radii of all open balls contained inside $\mathbb{U}$, and taking their union. The predecessor of $\mathbb{U}$ is an open set containing $\mathbb{U}$. The
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On the Kodaira problem for uniruled Kähler spaces Ark. Mat. (IF 0.7) Pub Date : 2020-10-01 Patrick Graf, Martin Schwald
We discuss the Kodaira problem for uniruled Kähler spaces. Building on a construction due to Voisin, we give an example of a uniruled Kähler space $X$ such that every run of the $K_X$-MMP immediately terminates with a Mori fibre space, yet $X$ does not admit an algebraic approximation. Our example also shows that for a Mori fibration, approximability of the base does not imply approximability of the
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Enveloping algebras with just infinite Gelfand–Kirillov dimension Ark. Mat. (IF 0.7) Pub Date : 2020-10-01 Natalia K. Iyudu, Susan J. Sierra
Let $\mathfrak{g}$ be the Witt algebra or the positive Witt algebra. It is well known that the enveloping algebra $U(\mathfrak{g})$ has intermediate growth and thus infinite Gelfand–Kirillov (GK-) dimension. We prove that the GK-dimension of $U(\mathfrak{g})$ is just infinite in the sense that any proper quotient of $U(\mathfrak{g})$ has polynomial growth. This proves a conjecture of Petukhov and the
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On the Hardy number of a domain in terms of harmonic measure and hyperbolic distance Ark. Mat. (IF 0.7) Pub Date : 2020-10-01 Christina Karafyllia
Let ψ be a conformal map on $\mathbb{D}$ with $\psi \left(0\right)=0$ and let ${F_{\alpha }}=\left\{z\in \mathbb{D}:\left|\psi \left(z\right)\right|=\alpha \right\}$ for $\alpha > 0$. Denote by ${H^{p}}\left(\mathbb{D}\right)$ the classical Hardy space with exponent $p > 0$ and by $\mathtt{h}\left(\psi \right)$ the Hardy number of ψ. Consider the limits \[L:=\underset{\alpha \to +\infty }{\lim }\left(\log