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Stability and instability of lattices in semisimple groups J. Anal. Math. (IF 1.0) Pub Date : 2023-12-22 Uri Bader, Alexander Lubotzky, Roman Sauer, Shmuel Weinberger
Using cohomological methods, we show that lattices in semisimple groups are typically stable with respect to the Frobenius norm but not with respect to the operator norm.
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On the Central Limit Theorem for linear eigenvalue statistics on random surfaces of large genus J. Anal. Math. (IF 1.0) Pub Date : 2023-12-22 Zeév Rudnick, Igor Wigman
We study the fluctuations of smooth linear statistics of Laplace eigenvalues of compact hyperbolic surfaces lying in short energy windows, when averaged over the moduli space of surfaces of a given genus. The average is taken with respect to the Weil–Petersson measure. We show that first taking the large genus limit, then a short window limit, the distribution tends to a Gaussian. The variance was
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Determinants of Laplacians on random hyperbolic surfaces J. Anal. Math. (IF 1.0) Pub Date : 2023-12-22 Frédéric Naud
For sequences (Xj) of random closed hyperbolic surfaces with volume Vol(Xj) tending to infinity, we prove that there exists a universal constant E > 0 such that for all ϵ > 0, the regularized determinant of the Laplacian satisfies $${{\log \det ({\Delta _{{X_j}}})} \over {{\rm{Vol}}({X_j})}} \in [E -\epsilon ,E +\epsilon]$$ with high probability as j → +⋡. This result holds for various models of random
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On the analytic theory of isotropic ternary quadratic forms J. Anal. Math. (IF 1.0) Pub Date : 2023-12-22 William Duke, Rainer Schulze-Pillot
A new local-global result about the primitive representations of zero by integral ternary quadratic forms is proven. By an extension of a result of Kneser (given in the Appendix), it yields a quantitative supplement to the Hasse principle on the number of automorphic orbits of primitive zeros of a genus of forms. One ingredient in its proof is an asymptotic formula for a count of the zeros of a given
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S1-bounded Fourier multipliers on H1(ℝ) and functional calculus for semigroups J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12
Abstract Let T: H1(ℝ) → H1(ℝ) be a bounded Fourier multiplier on the analytic Hardy space H1(ℝ) ⊂ L1(ℝ) and let m ∈ L∞(ℝ+) be its symbol, that is, \(\widehat {T(h)} = m\hat h\) for all h ∈ H1(ℝ). Let S1 be the Banach space of all trace class operators on ℓ2. We show that T admits a bounded tensor extension \(T\overline \otimes {I_{{S_1}}}:{H^1}(\mathbb{R};{S^1}) \to {H^1}(\mathbb{R};{S^1})\) if and
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Random polynomials in several complex variables J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Turgay Bayraktar, Thomas Bloom, Norm Levenberg
We generalize some previous results on random polynomials in several complex variables. A standard setting is to consider random polynomials \({H_n}(z): = \sum\nolimits_{j = 1}^{{m_n}} {{a_j}{p_j}} \) that are linear combinations of basis polynomials {pj} with i.i.d. complex random variable coefficients {aj} where {pj} form an orthonormal basis for a Bernstein-Markov measure on a compact set \(K \subset
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Quasilinear elliptic equations involving measure valued absorption terms and measure data J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Konstantinos T. Gkikas
Let 1 < p < N and Ω ⊂ ℝN be an open bounded domain. We study the existence of solutions to equation \((E) - {\Delta _p}u + g(u)\sigma = \mu \) in Ω, where g ∈ C(ℝ) is a nondecreasing function, μ is a bounded Radon measure on Ω and σ is a nonnegative Radon measure on ℝN. We show that if σ belongs to some Morrey space of signed measures, then we may investigate the existence of solutions to equation
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Universal eigenvalue statistics for dynamically defined matrices J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Arka Adhikari, Marius Lemm
We consider dynamically defined Hermitian matrices generated from orbits of the doubling map. We prove that their spectra fall into the GUE universality class from random matrix theory.
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The space of Hardy-weights for quasilinear equations: Maz’ya-type characterization and sufficient conditions for existence of minimizers J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Ujjal Das, Yehuda Pinchover
Let p ∈ (1, ∞) and Ω ⊂ ℝN be a domain. Let$$A: = ({a_{ij}}) \in L_{{\rm{loc}}}^\infty (\Omega;{\mathbb{R}^{N \times N}})$$ be a symmetric and locally uniformly positive definite matrix. Set$$|\xi |_A^2:\sum\limits_{i,j = 1}^N {{a_{ij}}(x){\xi _i}{\xi _j}},$$ ξ ∈ ℝN, and let V be a given potential in a certain local Morrey space. We assume that the energy functional$${Q_{p,A,V}}(\phi ): = \int_\Omega
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New vector solutions for the cubic nonlinear schrödinger system J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Lipeng Duan, Xiao Luo, Maoding Zhen
In this paper, we construct a family of new solutions for the following nonlinear Schrödinger system: $$\left\{{\matrix{{- \Delta u + P(y)u = \mu {u^3} + \beta u{\upsilon ^2},} & {u > 0,\,\,{\rm{in}}\,{\mathbb{R}^3},} \cr {- \Delta \upsilon + Q(y)\upsilon = v{\upsilon ^3} + \beta {u^2}\upsilon ,} & {\upsilon > 0,\,\,{\rm{in}}\,{\mathbb{R}^3},} \cr}} \right.$$ where P(y), Q(y) are positive radial potentials
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Asymptotics for Christoffel functions associated to continuum Schrödinger operators J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Benjamin Eichinger
We prove asymptotics of the Christoffel function, λL(ξ), of a continuum Schrödinger operator for points in the interior of the essential spectrum under some mild conditions on the spectral measure. It is shown that LλL(ξ) has a limit and that this limit is given by the Radon–Nikodym derivative of the spectral measure with respect to the Martin measure. Combining this with a recently developed local
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Oscillatory integral operators with homogeneous phase functions J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12
Abstract Oscillatory integral operators with 1-homogeneous phase functions satisfying a convexity condition are considered. For these we show the Lp–Lp-estimates for the Fourier extension operator of the cone due to Ou–Wang via polynomial partitioning. For this purpose, we combine the arguments of Ou–Wang with the analysis of Guth–Hickman–Iliopoulou, who previously showed sharp Lp–Lp-estimates for
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Symmetry breaking for ground states of biharmonic NLS via Fourier extension estimates J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Enno Lenzmann, Tobias Weth
We consider ground state solutions u ∈ H2(ℝN) of biharmonic (fourth-order) nonlinear Schrödinger equations of the form $${\Delta ^2}u + 2a\Delta u + bu - |u{|^{p - 2}}u = 0\,\,\,\,{\rm{in}}\,\,{\mathbb{R}^N}$$ with positive constants a, b > 0 and exponents 2 < p < 2*, where \({2^ * } = {{2N} \over {N - 4}}\) if N > 4 and 2* = ∞ if N ≤ 4. By exploiting a connection to the adjoint Stein–Tomas inequality
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Semiclassical states for a magnetic nonlinear Schrödinger equation with exponential critical growth in ℝ2 J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Pietro d’Avenia, Chao Ji
This paper is devoted to the magnetic nonlinear Schrödinger equation $${\left( {{\varepsilon \over i}\nabla - A(x)} \right)^2}u + V(x)u = f(|u{|^2})u\,\,{\rm{in}}\,\,{\mathbb{R}^2},$$ where ε > 0 is a parameter, V: ℝ2 → ℝ and A: ℝ2 → ℝ2 are continuous functions and f: ℝ → ℝ is a C1 function having exponential critical growth. Under a global assumption on the potential V, we use variational methods
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Quantitative behavior of unipotent flows and an effective avoidance principle J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Elon Lindenstrauss, Gregorii Margulis, Amir Mohammadi, Nimish A. Shah
We give an effective bound on how much time orbits of a unipotent group U on an arithmetic quotient G/Γ can stay near homogeneous subvarieties of G/Γ corresponding to ℚ-subgroups of G. In particular, we show that if such a U-orbit is moderately near a proper homogeneous subvariety of G/Γ for a long time, it is very near a different homogeneous subvariety. Our work builds upon the linearization method
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Semiclassical analysis of a nonlocal boundary value problem related to magnitude J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Heiko Gimperlein, Magnus Goffeng, Nikoletta Louca
We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy. Using recent techniques developed for pseudodifferential boundary problems we discuss the structure of the solution operator and resulting properties of the magnitude
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Scattering theory with unitary twists J. Anal. Math. (IF 1.0) Pub Date : 2023-12-12 Moritz Doll, Ksenia Fedosova, Anke Pohl
We study the spectral properties of the Laplace operator associated to a hyperbolic surface in the presence of a unitary representation of the fundamental group. Following the approach by Guillopé and Zworski, we establish a factorization formula for the twisted scattering determinant and describe the behavior of the scattering matrix in a neighborhood of 1/2.
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Infinite partial sumsets in the primes J. Anal. Math. (IF 1.0) Pub Date : 2023-12-01
Abstract We show that there exist infinite sets A = (a1, a2, …} and B = {b1, b2, …} of natural numbers such that ai + bj is prime whenever 1 ≤ i < j.
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The size of wild Kloosterman sums in number fields and function fields J. Anal. Math. (IF 1.0) Pub Date : 2023-12-01
Abstract We study p-adic hyper-Kloosterman sums, a generalization of the Kloosterman sum with a parameter k that recovers the classical Kloosterman sum when k = 2, over general p-adic rings and even equal characteristic local rings. These can be evaluated by a simple stationary phase estimate when k is not divisible by p, giving an essentially sharp bound for their size. We give a more complicated
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Insights on the Cesàro operator: shift semigroups and invariant subspaces J. Anal. Math. (IF 1.0) Pub Date : 2023-10-09 Eva A. Gallardo-Gutiérrez, Jonathan R. Partington
A closed subspace is invariant under the Cesàro operator \({\cal C}\) on the classical Hardy space \({H^2}(\mathbb{D})\) if and only if its orthogonal complement is invariant under the C0-semigroup of composition operators induced by the affine maps \({\varphi _t}(z) = {e^{ - t}}z + 1 - {e^{ - t}}\) for t ≥ 0 and \(z =\mathbb{D}\). The corresponding result also holds in the Hardy spaces Hp(\(\mathbb{D}\))
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The generalized anisotropic dynamical Wentzell heat equation with nonstandard growth conditions J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Carlos Carvajal-Ariza, Javier Henríquez-Amador, Alejandro Vélez-Santiago
Let Ω ⊆ ℝN be a bounded Lipschitz domain with the anisotropic extension property, for N ≥ 3. The aim of this paper is to establish the solvability and global regularity theory for a new class of generalized anisotropic heat-type boundary value problems involving the anisotropic \(\overrightarrow p ( \cdot )\)-Laplace operator \({\Delta _{\overrightarrow p ( \cdot )}}\), with (pure) dynamical anisotropic
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Bubbling solutions for mean field equations with variable intensities on compact Riemann surfaces J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Pablo Figueroa
For an asymmetric sinh-Poisson problem arising as a mean field equation of equilibrium turbulence vortices with variable intensities of interest in hydrodynamic turbulence, we address the existence of bubbling solutions on compact Riemann surfaces. By using a Lyapunov–Schmidt reduction, we find sufficient conditions under which there exist bubbling solutions blowing up at m different points of S: positively
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Generic Laplacian eigenfunctions on metric graphs J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Lior Alon
It is known that up to certain pathologies, a compact metric graph with standard vertex conditions has a Baire-generic set of choices of edge lengths such that all Laplacian eigenvalues are simple and have eigenfunctions that do not vanish at the vertices, [16, 12]. We provide a new notion of strong genericity, using subanalytic sets, that implies both Baire genericity and full Lebesgue measure. We
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The number of zeros of linear combinations of L-functions near the critical line J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Youness Lamzouri, Yoonbok Lee
In this paper, we investigate the zeros near the critical line of linear combinations of L-functions belonging to a large class, which conjecturally contains all L-functions arising from automorphic representations on GL(n). More precisely, if L1, …, LJ are distinct primitive L-functions with J ≥ 2, and bj are any non-zero real numbers, we prove that the number of zeros of \(F(s) = \sum\nolimits_{j
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A Fubini-type theorem for Hausdorff dimension J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Kornélia Héra, Tamás Keleti, András Máthé
It is well known that a classical Fubini theorem for Hausdorff dimension cannot hold; that is, the dimension of the intersections of a fixed set with a parallel family of planes do not determine the dimension of the set. Here we prove that a Fubini theorem for Hausdorff dimension does hold modulo sets that are small on all Lipschitz graphs. We say that \(G \subset {\mathbb{R}^k} \times {\mathbb{R}^n}\)
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On the supercritical fractional diffusion equation with Hardy-type drift J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Damir Kinzebulatov, Kodjo Raphaël Madou, Yuliy A. Semënov
We study the heat kernel of the supercritical fractional diffusion equation with the drift in the critical Hölder space. We show that such a drift can have point irregularities strong enough to make the heat kernel vanish at a point for all t > 0.
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Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Tomasz Jakubowski, Karol Szczypkowski
We investigate whether a fundamental solution of the Schrödinger equation ∂tu = (Δ + V)u has local in time sharp Gaussian estimates. We compare that class with the class of V for which local in time plain Gaussian estimates hold. We concentrate on V that have fixed sign and we present certain conclusions for V in the Kato class.
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Decomposing multitwists J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Alastair N. Fletcher, Vyron Vellis
The Decomposition Problem in the class \(LIP({\mathbb{S}^2})\) is to decompose any bi-Lipschitz map \(f:{\mathbb{S}^2} \to {\mathbb{S}^2}\) as a composition of finitely many maps of arbitrarily small isometric distortion. In this paper, we construct a decomposition for certain bi-Lipschitz maps which spiral around every point of a Cantor set X of Assouad dimension strictly smaller than one. These maps
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Local extrema for hypercube sections J. Anal. Math. (IF 1.0) Pub Date : 2023-10-05 Lionel Pournin
Consider the hyperplanes at a fixed distance t from the center of the hypercube [0, 1]d. Significant attention has been given to determining the hyperplanes H among these such that the (d − 1)-dimensional volume of H ∩ [0, 1]d is maximal or minimal. In the spirit of a question by Vitali Milman, the corresponding local problem is considered here when H is orthogonal to a diagonal or a sub-diagonal of
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Second order linear differential equations with a basis of solutions having only real zeros J. Anal. Math. (IF 1.0) Pub Date : 2023-08-30 Walter Bergweiler, Alexandre Eremenko, Lasse Rempe
Let A be a transcendental entire function of finite order. We show that, if the differential equation w″ + Aw = 0 has two linearly independent solutions with only real zeros, then the order of A must be an odd integer or one half of an odd integer. Moreover, A has completely regular growth in the sense of Levin and Pfluger. These results follow from a more general geometric theorem, which classifies
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Blaschke Products, Level Sets, and Crouzeix’s Conjecture J. Anal. Math. (IF 1.0) Pub Date : 2023-08-30 Kelly Bickel, Pamela Gorkin
We study several problems motivated by Crouzeix’s conjecture, which we consider in the special setting of model spaces and compressions of the shift with finite Blaschke products as symbols. We pose a version of the conjecture in this setting, called the level set Crouzeix (LSC) conjecture, and establish structural and uniqueness properties for (open) level sets of finite Blaschke products that allow
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Uniqueness theorems for weighted harmonic functions in the upper half-plane J. Anal. Math. (IF 1.0) Pub Date : 2023-08-30 Anders Olofsson, Jens Wittsten
We consider a class of weighted harmonic functions in the open upper half-plane known as α-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the real line and an appropriate vanishing condition at infinity. We find that the non-classical case (α ≠ 0) allows for a considerably more relaxed vanishing condition at
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Local large deviations for periodic infinite horizon Lorentz gases J. Anal. Math. (IF 1.0) Pub Date : 2023-08-30 Ian Melbourne, Françoise Pène, Dalia Terhesiu
We prove optimal local large deviations for the periodic infinite horizon Lorentz gas viewed as a ℤd-cover (d = 1,2) of a dispersing billiard. In addition to this specific example, we prove a general result for a class of nonuni-formly hyperbolic dynamical systems and observables associated with central limit theorems with nonstandard normalisation.
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Canonical systems whose Weyl coefficients have dominating real part J. Anal. Math. (IF 1.0) Pub Date : 2023-08-30 Matthias Langer, Raphael Pruckner, Harald Woracek
For a two-dimensional canonical system y′ (t) = zJH(t)y(t) on the half-line (0, ∞) whose Hamiltonian H is a.e. positive semi-definite, denote by qH its Weyl coefficient. De Branges’ inverse spectral theorem states that the assignment H ↦ qH is a bijection between Hamiltonians (suitably normalised) and Nevanlinna functions. The main result of the paper is a criterion when the singular integral of the
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Schwarz type lemmas and their applications in Banach spaces J. Anal. Math. (IF 1.0) Pub Date : 2023-07-18 Shaolin Chen, Hidetaka Hamada, Saminathan Ponnusamy, Ramakrishnan Vijayakumar
The main purpose of this paper is to develop some methods to investigate the Schwarz type lemmas of holomorphic mappings and pluriharmonic mappings in Banach spaces. Initially, we extend the classical Schwarz lemmas of holomorphic mappings to Banach spaces, and then we apply these extensions to establish a sharp Bloch type theorem for pluriharmonic mappings on homogeneous unit balls of ℂn and to obtain
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A note on Fourier restriction and nested Polynomial Wolff axioms J. Anal. Math. (IF 1.0) Pub Date : 2023-07-18 Jonathan Hickman, Joshua Zahl
This note records an asymptotic improvement on the known Lp range for the Fourier restriction conjecture in high dimensions. This is obtained by combining Guth’s polynomial partitioning method with recent geometric results regarding intersections of tubes with nested families of varieties.
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Transport of Gaussian measures with exponential cut-off for Hamiltonian PDEs J. Anal. Math. (IF 1.0) Pub Date : 2023-07-18 Giuseppe Genovese, Renato Lucà, Nikolay Tzvetkov
We show that introducing an exponential cut-off on a suitable Sobolev norm facilitates the proof of quasi-invariance of Gaussian measures with respect to Hamiltonian PDE flows and allows us to establish the exact Jacobi formula for the density. We exploit this idea in two different contexts, namely the periodic fractional Benjamin–Bona–Mahony (BBM) equation with dispersion β > 1 and the periodic one-dimensional
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The null set of a polytope, and the Pompeiu property for polytopes J. Anal. Math. (IF 1.0) Pub Date : 2023-07-18 Fabrício Caluza Machado, Sinai Robins
We study the null set \(N({\cal P})\) of the Fourier–Laplace transform of a polytope \({\cal P} \subset {\mathbb{R}^d}\), and we find that \(N({\cal P})\) does not contain (almost all) circles in ℝd. As a consequence, the null set does not contain the algebraic varieties {z ∈ ℂd ∣ z 21 + ⋯ + z 2d = α2} for each fixed α ∈ ℂ, and hence we get an explicit proof that the Pompeiu property is true for all
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An effective local-global principle and additive combinatorics in finite fields J. Anal. Math. (IF 1.0) Pub Date : 2023-07-18 Bryce Kerr, Jorge Mello, Igor E. Shparlinski
We use recent results about linking the number of zeros on algebraic varieties over ℂ, defined by polynomials with integer coefficients, and on their reductions modulo sufficiently large primes to study congruences with products and reciprocals of linear forms. This allows us to make some progress towards a question of B. Murphy, G. Petridis, O. Roche-Newton, M. Rudnev and I. D. Shkredov (2019) on
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Multiple solutions for two general classes of anisotropic systems with variable exponents J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Maria-Magdalena Boureanu
Abstract We are concerned with the weak solvability of two anisotropic systems with variable exponents: one with no-flux boundary condition, on a rectangular-like domain, and the other with zero Dirichlet boundary condition, on a general bounded domain. Both systems involve Leray–Lions type operators and a function F satisfying sublinear conditions at zero and infinity. By particularizing these general
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Causal sparse domination of Beurling maximal regularity operators J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Tuomas Hytönen, Andreas Rosén
We prove boundedness of Calderön–Zygmund operators acting in Banach function spaces on domains, defined by the L1 Carleson functional and Lq (1 < q < ∞) Whitney averages. For such bounds to hold, we assume that the operator maps towards the boundary of the domain. We obtain the Carleson estimates by proving a pointwise domination of the operator, by sparse operators with a causal structure. The work
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Scaling limits of fluctuations of extended-source internal DLA J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 David Darrow
In a previous work, we showed that the 2D, extended-source internal DLA (IDLA) of Levine and Peres is δ3/5-close to its scaling limit, if δ is the lattice size. In this paper, we investigate the scaling limits of the fluctuations themselves. Namely, we show that two naturally defined error functions, which measure the “lateness” of lattice points at one time and at all times, respectively, converge
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Continuity of the Temperature in a Multi-Phase Transition Problem. Part III J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Ugo Gianazza, Naian Liao
We establish local continuity of locally bounded weak solutions to a doubly nonlinear parabolic equation that models the temperature in multi-phase transitions. The enthalpy allows for general maximal monotone graphs of the temperature. Remarkably, moduli of continuity can be estimated without an explicit form of the enthalpy.
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Translates of S-arithmetic periodic orbits and applications J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Uri Shapira, Cheng Zheng
We prove that certain sequences of periodic orbits of the diagonal group in the space of lattices equidistribute. As an application we obtain new information regarding the sequence of best approximations to certain vectors with algebraic coordinates. In order to prove these results we generalize the seminal work of Eskin, Mozes and Shah about the equidistribution of translates of periodic measures
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On isomorphisms between ideals of Fourier algebras of finite abelian groups J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Alan Czuroń, Michał Wojciechowski
We study linear isomorphisms between the ideals of Fourier algebras A(G1) and A(G2) where \(\widehat{{G_1}}\) and \(\widehat{{G_2}}\) are infinite compact abelian torsion groups, assuming that there exists a infinite subgroup of G1 non-isomorphic to any subgroup of G2. Then ∥Tn∥ → ∞ for any sequences of ideals I (n)2 ⊂ A(G2), and any increasing sequence of ideals I (n)1 ⊂ A(G1) such that \(\overline
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On wavelet polynomials and Weyl multipliers J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Anna Kamont, Grigori A. Karagulyan
For the wavelet type orthonormal systems ϕn, we establish a new bound $${\left\| {\mathop {\max}\limits_{1 \le m \le n} \left| {\sum\limits_{j \in {G_m}} {\langle f,{\phi _j}\rangle} {\phi _j}} \right|} \right\|_p} \mathbin{\lower.3ex\hbox{$\buildrel<\over{\smash{\scriptstyle\sim}\vphantom{_x}}$}} \sqrt {\log (n + 1)} \cdot ||f||{_p},\,\,\,\,\,\,1
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Surjectivity of linear operators and semialgebraic global diffeomorphisms J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Francisco Braun, Luis Renato Goncalves Dias, Jean Venato-Santos
We prove that a C∞ semialgebraic local diffeomorphism of ℝn with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if n − 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of ℝn. Our conjecture implies a very known conjecture of Z. Jelonek. We further relate the surjectivity
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Modified scattering for the fractional nonlinear Schrödinger equation with $$\alpha \in ({3 \over 2},2)$$ J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Nakao Hayashi, Pavel I. Naumkin, Isahi Sánchez-Suárez
We study the Cauchy problem for the fractional nonlinear Schrödinger equation $$\left\{{\matrix{{i{\partial _t}u + {1 \over \alpha}{{\left| {{\partial _x}} \right|}^\alpha}u = \lambda |u{|^2}u,\,\,t>0,} \hfill\;\;\;\;\;\;\;\;\;\;\;\; {x \in \mathbb{R},} \hfill \cr {u(0,x) = {u_0}(x),} \hfill\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{x \in \mathbb{R},} \hfill \cr}} \right
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The Stein–Tomas inequality under the effect of symmetries J. Anal. Math. (IF 1.0) Pub Date : 2023-06-20 Rainer Mandel, Diogo Oliveira e Silva
We prove new Fourier restriction estimates to the unit sphere \({\mathbb{S}^{d-1}}\) on the class of O(d − k) × O(k)-symmetric functions, for every d ≥ 4 and 2 ≤ k ≤ d − 2. As an application, we establish the existence of maximizers for the endpoint Stein–Tomas inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp.
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Connection coefficients for ultraspherical polynomials with argument doubling and generalized bispectrality J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Maxim Derevyagin, Jeffrey S. Geronimo
We start by presenting a generalization of a discrete wave equation that is satisfied by the entries of the matrix coefficients of the refinement equation corresponding to the multiresolution analysis of Alpert. The entries are functions of two discrete variables and they can be expressed in terms of the Legendre polynomials. Next, we generalize these functions to the case of the ultraspherical polynomials
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Bounds for theta sums in higher rank. I J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Jens Marklof, Matthew Welsh
Theta sums are finite exponential sums with a quadratic form in the oscillatory phase. This paper establishes new upper bounds for theta sums in the case of smooth and box truncations. This generalises a classic 1977 result of Fiedler, Jurkat and Körner for one-variable theta sums and, in the multi-variable case, improves previous estimates obtained by Cosentino and Flaminio in 2015. Key steps in our
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Arithmetic subtrees in large subsets of products of trees J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Kamil Bulinski, Alexander Fish
Furstenberg-Weiss have extended Szemerédi’s theorem on arithmetic progressions to trees by showing that a large subset of the tree contains arbitrarily long arithmetic subtrees. We study higher dimensional versions that analogously extend the multidimensional Szemerédi theorem by demonstrating the existence of certain arithmetic structures in large subsets of a cartesian product of trees.
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Geometric characterizations for conformal mappings in weighted Bergman spaces J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Christina Karafyllia, Nikolaos Karamanlis
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of conformal mappings in Hardy or weighted Bergman spaces by studying Euclidean areas. Applying these results, we prove several consequences for such mappings that extend
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Signed quasiregular curves J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Susanna Heikkilä
We define a subclass of quasiregular curves, called signed quasiregular curves, which contains holomorphic curves and quasiregular mappings. As our main result, we prove a growth theorem of Bonk—Heinonen type for signed quasiregular curves. To obtain our main result, we prove that signed quasiregular curves satisfy a weak reverse Hölder inequality and that this weak reverse Hölder inequality implies
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Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Anders Björn, Jana Björn, Juha Lehrbäck
In a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality, we prove sharp growth and integrability results for p-harmonic Green functions and their minimal p-weak upper gradients. We show that these properties are determined by the growth of the underlying measure near the singularity. Corresponding results are obtained also for more general p-harmonic functions
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Dimension-free LP-estimates for vectors of Riesz transforms in the rational Dunkl setting J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Agnieszka Hejna
In this article, we prove a dimension-free upper bound for the Lp-norms of the vector of Riesz transforms in the rational Dunkl setting. Our main technique is the Bellman function method adapted to the Dunkl setting.
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Quantitative disjointness of nilflows from horospherical flows J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Asaf Katz
We prove a quantitative variant of a disjointness theorem of nilflows from horospherical flows following a technique of Venkatesh, combined with the structural theorems for nilflows by Green, Tao and Ziegler.
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Testing families of analytic discs in the unit ball of ℂ2 J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Luca Baracco, Stefano Pinton
Let a, b, c ∈ ℂ2 be three non-collinear points such that their mutual joining complex lines do not intersect the unit ball \(\mathbb{B}^{2}\) and such that the line through a and b is tangent to \(\mathbb{B}^{2}\). Then the set of lines concurrent to a, b or c is a testing family for continuous functions on \(\mathbb{S}^{3}\). This improves a result by the authors and solves a case left open in the
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A Faber-Krahn inequality for mixed local and nonlocal operators J. Anal. Math. (IF 1.0) Pub Date : 2023-03-20 Stefano Biagi, Serena Dipierro, Enrico Valdinoci, Eugenio Vecchi
We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn inequality. More precisely, we show that balls minimize the first eigenvalue among sets of given volume and we provide a stability result for sets that almost attain the minimum.
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A sharp L10 decoupling for the twisted cubic J. Anal. Math. (IF 1.0) Pub Date : 2023-01-05 Hongki Jung
We prove a sharp l10(L10) decoupling for the moment curve in ℝ3. The proof involves a two-step decoupling combined with new incidence estimates for planks, tubes and plates.