Journal of Functional Analysis最新文献

英文中文

A Weyl law for the p-Laplacian p 拉普拉斯的韦尔定律

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-11-06 DOI: 10.1016/j.jfa.2024.110734

Liam Mazurowski

We show that a Weyl law holds for the variational spectrum of the p-Laplacian. More precisely, let

{(λ_{i})}_{i = 1}^{\infty}

be the variational spectrum of

Δ_{p}

on a closed Riemannian manifold

(X, g)

and let

N (λ) = # {i : λ_{i} < λ}

be the associated counting function. Then we have a Weyl law

N (λ) \sim c vol (X) λ^{n / p} .

This confirms a conjecture of Friedlander. The proof is based on ideas of Gromov [5] and Liokumovich, Marques, Neves [7].

我们证明，p-拉普拉斯的变谱存在韦尔定律。更确切地说，设 (λi)i=1∞ 为封闭黎曼流形 (X,g) 上 Δp 的变分谱，设 N(λ)=#{i:λi<λ} 为相关的计数函数。那么我们就有一个韦尔定律N(λ)∼cvol(X)λn/p。这证实了弗里德兰德的猜想。证明基于 Gromov [5] 和 Liokumovich, Marques, Neves [7] 的观点。

引用次数: 0

The Fourier transform on valuations is the Fourier transform 估值的傅立叶变换是傅立叶变换

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-11-06 DOI: 10.1016/j.jfa.2024.110741

Dmitry Faifman , Thomas Wannerer

Alesker has proved the existence of a remarkable isomorphism of the space of translation-invariant smooth valuations that has the same functorial properties as the classical Fourier transform. In this paper, we show how to directly describe this isomorphism in terms of the Fourier transform on functions. As a consequence, we obtain simple proofs of the main properties of the Alesker–Fourier transform. One of these properties was previously only conjectured by Alesker and is proved here for the first time.

阿列斯克证明了平移不变光滑值空间存在一个显著的同构，它具有与经典傅里叶变换相同的函数性质。在本文中，我们展示了如何直接用函数的傅里叶变换来描述这种同构。因此，我们得到了 Alesker-Fourier 变换主要性质的简单证明。其中一个性质以前只是阿莱克斯克的猜想，本文首次证明了它。

引用次数: 0

Lipschitz truncation method for parabolic double-phase systems and applications 抛物线双相系统的 Lipschitz 截断法及其应用

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-11-05 DOI: 10.1016/j.jfa.2024.110738

Wontae Kim, Juha Kinnunen, Lauri Särkiö

We discuss a Lipschitz truncation technique for parabolic double-phase problems of p-Laplace type in order to prove energy estimates and uniqueness results for the Dirichlet problem. Moreover, we show existence for a non-homogeneous double-phase problem. The Lipschitz truncation method is based on a Whitney-type covering result and a related partition of unity in the intrinsic geometry for the double-phase problem.

我们讨论了 p-Laplace 型抛物线双相问题的 Lipschitz 截断技术，以证明 Dirichlet 问题的能量估计和唯一性结果。此外，我们还证明了非均质双相问题的存在性。Lipschitz截断方法基于惠特尼型覆盖结果和双相问题内在几何中的相关统一分割。

引用次数: 0

Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries 完全互不相连的局部紧凑群在其边界上的作用的交叉积的简单性

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-11-05 DOI: 10.1016/j.jfa.2024.110732

Ryoya Arimoto

We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial converse of this result.

我们证明，如果一个完全断开的局部紧凑群具有拓扑自由边界，那么该群在其弗斯滕伯格边界上的连续函数的还原交叉积是简单的。我们还证明了这一结果的部分反证。

引用次数: 0

Corrigendum to “Mourre theory for analytically fibered operators” [J. Funct. Anal. 152 (1) (1998) 202–219] 对 "分析纤维化算子的穆尔勒理论 "的更正 [J. Funct. Anal. 152 (1) (1998) 202-219]

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-30 DOI: 10.1016/j.jfa.2024.110697

F. Nier , C. Gérard

引用次数: 0

On the Hankel transform of Bessel functions on complex numbers and explicit spectral formulae over the Gaussian field 关于复数上贝塞尔函数的汉克尔变换和高斯域上的明确谱公式

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-28 DOI: 10.1016/j.jfa.2024.110723

Zhi Qi

In this paper, on the complex field

C

, we prove two integral formulae for the Hankel–Mellin transform and the double Fourier–Mellin transform of Bessel functions, both resulting the hypergeometric function. As two applications, we use the former integral formula to make explicit the spectral formula of Bruggeman and Motohashi for the fourth moment of Dedekind zeta function over the Gaussian number field

Q (i)

and to establish a spectral formula for the Hecke-eigenvalue twisted second moment of central L-values for the Picard group

{PGL}_{2} (Z [i])

. Moreover, we develop the theory of distributional Hankel transform on

C ∖ {0}

本文在复数场 C 上证明了贝塞尔函数的汉克尔-梅林变换和双傅里叶-梅林变换的两个积分公式，这两个积分公式都产生了超几何函数。作为两个应用，我们利用前一个积分公式明确了布鲁格曼和本桥对高斯数域 Q(i) 的 Dedekind zeta 函数第四矩的谱公式，并建立了皮卡组 PGL2(Z[i]) 的赫克特征值扭转中心 L 值第二矩的谱公式。此外，我们还发展了 C∖{0} 上的分布汉克尔变换理论。

引用次数: 0

Sequential commutation in tracial von Neumann algebras 迹冯诺依曼代数的顺序交换

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-28 DOI: 10.1016/j.jfa.2024.110719

Srivatsav Kunnawalkam Elayavalli, Gregory Patchell

Recall that a unitary in a tracial von Neumann algebra is Haar if

τ (u^{n}) = 0

for all

n \in N

. We introduce and study a new Borel equivalence relation

\sim_{N}

on the set of Haar unitaries in a diffuse tracial von Neumann algebra N. Two Haar unitaries

u, v

U (N)

are related if there exists a finite path of sequentially commuting Haar unitaries in an ultrapower

N^{U}

, beginning at u and ending at v. We show that for any diffuse tracial von Neumann algebra N, the equivalence relation

\sim_{N}

admits either 1 orbit or uncountably many orbits. We characterize property Gamma in terms of path length and number of orbits of

\sim_{N}

and also show the existence of non-Gamma II₁ factors so that

\sim_{N}

admits only 1 orbit. Examples where

\sim_{N}

admits uncountably many orbits include N having positive 1-bounded entropy:

h (N) > 0

. As a key example, we explicitly describe

\sim_{L (F_{t})}

for the free group factors. Using these ideas we introduce a natural numerical invariant for diffuse tracial von Neumann algebras called the commutation diameter, with applications to elementary equivalence classification. This computes the largest value of the minimal path length over related unitaries. We show that if N admits one orbit, then the commutation diameter is finite and moreover is an elementary equivalence invariant. By studying the finer technical structure of lifts of certain commutators in ultrapowers we obtain non-trivial lower bounds for the family of arbitrary graph products N of diffuse tracial von Neumann algebras whose underlying graph is connected and has diameter at least 4, and distinguish them up to elementary equivalence from the [12] exotic factors, despite satisfying

h (N) \leq 0

回想一下，当对所有n∈n τ(un)=0时，迹von Neumann代数中的酉是Haar。我们在扩散迹迹冯·诺伊曼代数N中的Haar酉集上引入并研究了一个新的Borel等价关系~ N，如果在超幂次NU中存在从u开始到v结束的顺序交换Haar酉集的有限路径，则u (N)中的两个Haar酉集u，v是相关的。我们证明了对于任何扩散迹迹冯·诺伊曼代数N，等价关系~ N允许1个轨道或不可数多个轨道。我们用~ N的路径长度和轨道数来描述性质Gamma，并且还证明了非Gamma II1因子的存在，因此~ N只允许1个轨道。在~ N允许不可数轨道的例子中，N有正的1界熵：h(N)>0。作为一个关键的例子，我们明确地描述了自由群因子的~ L（Ft）。利用这些思想，我们引入了漫射迹迹冯·诺伊曼代数的一个自然数值不变量，称为交换直径，并将其应用于初等等价分类。这将计算相关一元上最小路径长度的最大值。我们证明了如果N允许一个轨道，那么换易直径是有限的，并且是初等等价不变量。通过研究超功率中某些换向子的升力的精细技术结构，得到了底图连通且直径至少为4的漫射迹迹von Neumann代数的任意图积N族的非平凡下界，并在满足h(N)≤0的情况下，将其与[12]奇异因子区分为初等等价。

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引用次数: 0

Weighted Dirichlet spaces that are de Branges-Rovnyak spaces with equivalent norms 具有等效规范的 de Branges-Rovnyak 空间的加权 Dirichlet 空间

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-24 DOI: 10.1016/j.jfa.2024.110717

Stamatis Pouliasis

For a positive Borel measure μ in the unit disc, we examine which weighted Dirichlet spaces

D_{μ}

can be identified with de Branges-Rovnyak spaces

H_{b}

, with equivalent norms. We prove a necessary condition for the equality

D_{μ} = H_{b}

and we explore its consequences. For Carleson measures μ, we give a necessary and sufficient condition for the equality

D_{μ} = H_{b_{μ}}

, for a certain outer function

b_{μ}

related with the balayage of μ on the unit circle, and we provide examples of those spaces.

对于单位圆盘中的正伯勒量μ，我们研究了哪些加权德里赫特空间 Dμ 可以与具有等效规范的 de Branges-Rovnyak 空间 Hb 标识。我们证明了 Dμ=Hb 相等的必要条件，并探讨了其后果。对于卡莱森量μ，我们给出了Dμ=Hbμ相等的必要条件和充分条件，条件是与单位圆上μ的巴拉维相关的某个外函数bμ，我们还提供了这些空间的例子。

引用次数: 0

On boundedness of isomerization paths for non- and semirelativistic molecules 论非相对论分子和半相对论分子异构化路径的有界性

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-24 DOI: 10.1016/j.jfa.2024.110713

Ioannis Anapolitanos , Marco Olivieri , Sylvain Zalczer

This article focuses on isomerizations of molecules, i.e. chemical reactions during which a molecule is transformed into another one with atoms in a different spatial configuration. We consider the special case in which the system breaks into two submolecules whose internal geometry is solid during the whole procedure. We prove, under some conditions, that the distance between the two submolecules stays bounded during the reaction. This paper extends [Anapolitanos-Lewin, 2020] in two directions. The first one is that we relax assumptions that the ground state eigenspaces of the submolecules have to fulfill. The second one is that we allow semirelativistic kinetic energy as well. We provide an asymptotic expansion of the interaction energy between two molecules, including multipolar interactions and the van der Waals attraction. In addition to this static result, we proceed to a quasistatic analysis to investigate the variation of the energy when the nuclei move.

本文的重点是分子的异构化，即在化学反应过程中，一个分子转变为另一个具有不同空间构型原子的分子。我们考虑了一种特殊情况，即在整个反应过程中，体系分裂成两个内部几何形状为固态的子分子。我们证明，在某些条件下，两个子分子之间的距离在反应过程中保持有界。本文在两个方向上扩展了[Anapolitanos-Lewin, 2020]。首先，我们放宽了亚分子基态特征空间必须满足的假设条件。第二，我们也允许半惯性动能。我们提供了两个分子之间相互作用能量的渐近展开，包括多极相互作用和范德华吸引力。除了这一静态结果，我们还进行了准静态分析，以研究原子核移动时的能量变化。

引用次数: 0

Operator ℓp → ℓq norms of random matrices with iid entries 具有 iid 条目的随机矩阵的运算符 ℓp → ℓq 准则

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-10-24 DOI: 10.1016/j.jfa.2024.110720

Rafał Latała, Marta Strzelecka

<div><div>We prove that for every <math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math> and every random matrix <math><mi>X</mi><mo>=</mo><msub><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>i</mi><mo>≤</mo><mi>m</mi><mo>,</mo><mi>j</mi><mo>≤</mo><mi>n</mi></mrow></msub></math> with iid centered entries satisfying the α-regularity assumption <math><msub><mrow><mo>‖</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mn>2</mn><mi>ρ</mi></mrow></msub><mo>≤</mo><mi>α</mi><msub><mrow><mo>‖</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>ρ</mi></mrow></msub></math> for every <math><mi>ρ</mi><mo>≥</mo><mn>1</mn></math>, the expectation of the operator norm of X from <math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math> to <math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msubsup></math> is comparable, up to a constant depending only on α, to<math><msup><mrow><mi>m</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>q</mi></mrow></msup><munder><mi>sup</mi><mrow><mi>t</mi><mo>∈</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msubsup></mrow></munder><mo>⁡</mo><msub><mrow><mo>‖</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><msub><mrow><mi>t</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>j</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>q</mi><mo>∧</mo><mi>Log</mi><mspace></mspace><mi>m</mi></mrow></msub><mo>+</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>1</mn><mo>/</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow></msup><munder><mi>sup</mi><mrow><mi>s</mi><mo>∈</mo><msubsup><mrow><mi>B</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mo>⁎</mo></mrow></msup></mrow><mrow><mi>m</mi></mrow></msubsup></mrow></munder><mo>⁡</mo><msub><mrow><mo>‖</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>∧</mo><mi>Log</mi><mspace></mspace><mi>n</mi></mrow></msub><mo>.</mo></math> We give more explicit formulas, expressed as exact functions of p, q, m, and n, for the two-sided bounds of the operator norms in the case when the entries <math><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math> are: Gaussia

我们证明，对于每个 p,q∈[1,∞]和每个随机矩阵 X=(Xi,j)i≤m,j≤n，其 iid 居中条目满足α正则假设‖Xi,j‖2ρ≤α‖Xi,j‖ρ，对于每个 ρ≥1、从 ℓpn 到 ℓqm 的 X 的算子规范的期望是可比的，直到一个只取决于 α 的常数，tom1/qsupt∈Bpn‖∑j=1ntjX1,j‖q∧Logm+n1/p⁎sups∈Bq⁎m‖∑i=1msiXi,1‖p⁎∧Logn。我们给出了更明确的公式，用 p、q、m 和 n 的精确函数表示了当条目 Xi,j 为以下情况时算子规范的双侧边界：高斯、魏布里安、对数凹尾和对数凸尾。在 1≤q≤2≤p 的范围内，我们提供了较弱正则假设 (EX1,14)1/4≤α(EX1,12)1/2 下的双侧边界。

引用次数: 0

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