Journal of Functional Analysis最新文献_第3页

Limit formulas for norms of tensor power operators 张量幂算子范数的极限公式

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-07-02 DOI: 10.1016/j.jfa.2025.111113

Guillaume Aubrun , Alexander Müller-Hermes

引用次数: 0

The spectral gap of a Gaussian quantum Markovian generator 高斯量子马尔可夫发生器的谱隙

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-07-02 DOI: 10.1016/j.jfa.2025.111119

F. Fagnola, D. Poletti, E. Sasso, V. Umanità

{"title":"The spectral gap of a Gaussian quantum Markovian generator","authors":"F. Fagnola, D. Poletti, E. Sasso, V. Umanità","doi":"10.1016/j.jfa.2025.111119","DOIUrl":"10.1016/j.jfa.2025.111119","url":null,"abstract":"<div><div>Gaussian quantum Markov semigroups are the natural non-commutative extension of classical Ornstein-Uhlenbeck semigroups. They arise in open quantum systems of bosons where canonical non-commuting random variables of positions and momenta come into play. If there exists a faithful invariant density we explicitly compute the optimal exponential convergence rate, namely the spectral gap of the generator, in non-commutative <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> spaces determined by the invariant density showing that the exact value is the lowest eigenvalue of a certain matrix determined by the diffusion and drift matrices. The spectral gap turns out to depend on the non-commutative <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> space considered, whether the one determined by the so-called GNS or KMS multiplication by the square root of the invariant density. In the first case, it is strictly positive if and only if there is the maximum number of linearly independent noises. While, we exhibit explicit examples in which it is strictly positive only with KMS multiplication. We do not assume any symmetry or quantum detailed balance condition with respect to the invariant density.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111119"},"PeriodicalIF":1.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

One-sided Muckenhoupt weights and one-sided weakly porous sets in R 单侧Muckenhoupt权值和单侧弱多孔集

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-07-02 DOI: 10.1016/j.jfa.2025.111110

Hugo Aimar , Ivana Gómez , Ignacio Gómez Vargas , Francisco Javier Martín-Reyes

{"title":"One-sided Muckenhoupt weights and one-sided weakly porous sets in R","authors":"Hugo Aimar , Ivana Gómez , Ignacio Gómez Vargas , Francisco Javier Martín-Reyes","doi":"10.1016/j.jfa.2025.111110","DOIUrl":"10.1016/j.jfa.2025.111110","url":null,"abstract":"<div><div>In this work, we introduce the geometric concept of one-sided weakly porous sets in the real line and show that a set <span><math><mi>E</mi><mo>⊂</mo><mi>R</mi></math></span> satisfies <span><math><mi>d</mi><msup><mrow><mo>(</mo><mo>⋅</mo><mo>,</mo><mi>E</mi><mo>)</mo></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup><mo>∈</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mi>R</mi><mo>)</mo><mo>∩</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mtext>loc</mtext></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> for some <span><math><mi>α</mi><mo>></mo><mn>0</mn></math></span> if and only if <em>E</em> is right-sided weakly porous. Furthermore, we find that the property of being both left-sided and right-sided weakly porous is equivalent to the recent weakly porous condition discussed in the bibliography, which, in turn, was previously found to be intimately related to the usual class of Muckenhoupt weights <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111110"},"PeriodicalIF":1.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Random geometric graphs in reflexive Banach spaces 自反Banach空间中的随机几何图

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-07-02 DOI: 10.1016/j.jfa.2025.111112

József Balogh , Mark Walters , András Zsák

{"title":"Random geometric graphs in reflexive Banach spaces","authors":"József Balogh , Mark Walters , András Zsák","doi":"10.1016/j.jfa.2025.111112","DOIUrl":"10.1016/j.jfa.2025.111112","url":null,"abstract":"<div><div>We investigate a random geometric graph model introduced by Bonato and Janssen. The vertices are the points of a countable dense set <em>S</em> in a (necessarily separable) normed vector space <em>X</em>, and each pair of points are joined independently with some fixed probability <em>p</em> (with <span><math><mn>0</mn><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn></math></span>) if they are less than distance 1 apart. A countable dense set <em>S</em> in a normed space is <em>Rado</em>, if the resulting graph is almost surely unique up to isomorphism: that is any two such graphs are, almost surely, isomorphic.</div><div>Not surprisingly, understanding which sets are Rado is closely related to the geometry of the underlying normed space. It turns out that a key question is in which spaces must step-isometries (maps that preserve the integer parts of distances) on dense subsets necessarily be isometries. We answer this question for a large class of Banach spaces including all strictly convex reflexive spaces. In the process we prove results on the interplay between the norm topology and weak topology that may be of independent interest.</div><div>As a consequence of these Banach space results we show that almost all countable dense sets in strictly convex reflexive spaces are strongly non-Rado (that is, any two graphs are almost surely non-isomorphic). However, we show that there do exist Rado sets even in <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. Finally we construct a Banach space in which all countable dense set are strongly non-Rado.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111112"},"PeriodicalIF":1.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A quantitative Gidas-Ni-Nirenberg-type result for the p-Laplacian via integral identities 基于积分恒等式的p- laplace的一个定量gidas - ni - nirenberg型结果

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-26 DOI: 10.1016/j.jfa.2025.111108

Serena Dipierro , João Gonçalves da Silva , Giorgio Poggesi , Enrico Valdinoci

{"title":"A quantitative Gidas-Ni-Nirenberg-type result for the p-Laplacian via integral identities","authors":"Serena Dipierro , João Gonçalves da Silva , Giorgio Poggesi , Enrico Valdinoci","doi":"10.1016/j.jfa.2025.111108","DOIUrl":"10.1016/j.jfa.2025.111108","url":null,"abstract":"<div><div>We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the <em>p</em>-Laplacian.</div><div>Quantitative stability is achieved here via integral identities based on the proof of rigidity established by J. Serra in 2013, which extended to general dimension and the <em>p</em>-Laplacian operator an argument proposed by P.-L. Lions in dimension 2 for the classical Laplacian.</div><div>Stability results for the classical Gidas-Ni-Nirenberg symmetry theorem (involving the classical Laplacian) via the method of moving planes were established by Rosset in 1994 and by Ciraolo, Cozzi, Perugini, Pollastro in 2024.</div><div>To the authors' knowledge, the present paper provides the first quantitative Gidas-Ni-Nirenberg-type result involving the <em>p</em>-Laplacian for <span><math><mi>p</mi><mo>≠</mo><mn>2</mn></math></span>. Even for the classical Laplacian (i.e., for <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>), this is the first time that integral identities are used to achieve stability for a Gidas-Ni-Nirenberg-type result.</div><div>In passing, we obtain a quantitative estimate for the measure of the singular set and an explicit uniform gradient bound.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111108"},"PeriodicalIF":1.7,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144536014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Anderson localization for CMV matrices with Verblunsky coefficients defined by the hyperbolic toral automorphism 由双曲总自同构定义的具有Verblunsky系数的CMV矩阵的Anderson定位

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-19 DOI: 10.1016/j.jfa.2025.111103

Yanxue Lin , Shuzheng Guo , Daxiong Piao

引用次数: 0

Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction 具有奇异相互作用的无限多粒子非线性Hartree方程的全局适定性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111102

Sonae Hadama , Younghun Hong

引用次数: 0

Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms 一类Sobolev范数和BV范数的非局部近似的极限估计

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111106

Massimo Gobbino, Nicola Picenni

引用次数: 0

Calculus for parametric boundary problems with global projection conditions 具有全局投影条件的参数边界问题的微积分

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111099

Jörg Seiler

引用次数: 0

Non existence and strong ill-posedness in H2 for the stable IPM equation 稳定IPM方程在H2中的不存在性和强病态性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111097

Roberta Bianchini , Diego Córdoba , Luis Martínez-Zoroa

{"title":"Non existence and strong ill-posedness in H2 for the stable IPM equation","authors":"Roberta Bianchini , Diego Córdoba , Luis Martínez-Zoroa","doi":"10.1016/j.jfa.2025.111097","DOIUrl":"10.1016/j.jfa.2025.111097","url":null,"abstract":"<div><div>We prove the non-existence and strong ill-posedness of the Incompressible Porous Media (IPM) equation for initial data that are small <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> perturbations of the linearly stable profile <span><math><mo>−</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. A remarkable novelty of the proof is the construction of an <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> perturbation, which solves the IPM equation and neutralizes the stabilizing effect of the background profile near the origin, where a strong deformation leading to non-existence in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is created. This strong deformation is achieved through an iterative procedure inspired by the work of Córdoba and Martínez-Zoroa (2022) <span><span>[7]</span></span>. However, several differences - beyond purely technical aspects - arise due to the anisotropic and, more importantly, to the partially dissipative nature of the equation, adding further challenges to the analysis.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111097"},"PeriodicalIF":1.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0