Journal of Functional Analysis最新文献_第10页

Higher relative index theorems for foliations 叶化的高相对指数定理

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-17 DOI: 10.1016/j.jfa.2025.111098

Moulay Tahar Benameur , James L. Heitsch

{"title":"Higher relative index theorems for foliations","authors":"Moulay Tahar Benameur , James L. Heitsch","doi":"10.1016/j.jfa.2025.111098","DOIUrl":"10.1016/j.jfa.2025.111098","url":null,"abstract":"<div><div>In this paper we solve the general case of the cohomological relative index problem for foliations of non-compact manifolds. In particular, we significantly generalize the groundbreaking results of Gromov and Lawson, [20], to Dirac operators defined along the leaves of foliations of non-compact complete Riemannian manifolds, by involving all the terms of the Connes-Chern character, especially the higher order terms in Haefliger cohomology. The zero-th order term corresponding to holonomy invariant measures was carried out in [8] and becomes a special case of our main results here. In particular, for two leafwise Dirac operators on two foliated manifolds which agree near infinity, we define a relative topological index and the Connes-Chern character of a relative analytic index, both being in relative Haefliger cohomology. We show that these are equal. This invariant can be paired with closed holonomy invariant currents (which agree near infinity) to produce higher relative scalar invariants. When we relate these invariants to the leafwise index bundles, we restrict to Riemannian foliations on manifolds of sub-exponential growth. This allows us to prove a higher relative index bundle theorem, extending the classical index bundle theorem of [5]. Finally, we construct examples of foliations and use these invariants to prove that their spaces of leafwise positive scalar curvature metrics have infinitely many path-connected components, completely new results which are not available from [8]. In particular, these results confirm the well-known idea that important geometric information of foliations is embodied in the higher terms of the <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> genus.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111098"},"PeriodicalIF":1.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313217","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

Martingale suitable weak solutions of 3-D stochastic Navier-Stokes equations with vorticity bounds 具有涡度界的三维随机Navier-Stokes方程的鞅适弱解

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111081

Weiquan Chen , Zhao Dong

{"title":"Martingale suitable weak solutions of 3-D stochastic Navier-Stokes equations with vorticity bounds","authors":"Weiquan Chen , Zhao Dong","doi":"10.1016/j.jfa.2025.111081","DOIUrl":"10.1016/j.jfa.2025.111081","url":null,"abstract":"<div><div>We construct martingale suitable weak solutions for 3-dimensional incompressible stochastic Navier-Stokes equations with generally non-linear noise. In deterministic setting, as widely known, “suitable weak solutions” are Leray-Hopf weak solutions enjoying two different types of local energy inequalities (LEIs). In stochastic setting, we apply the idea of “martingale solution”, avoid transforming to random system, and show new stochastic versions of the two local energy inequalities. In particular, in additive and linear multiplicative noise case, OU-processes and the exponential formulas DO NOT play a role in our formulation of LEIs. This is different to <span><span>[16]</span></span>, <span><span>[44]</span></span> where the additive noise case is dealt. Also, we successfully apply the concept of “a.e. super-martingale” to describe this local energy behavior. To relate the well-known “dissipative weak solutions” come up with in <span><span>[12]</span></span>, we derive a local energy equality and extend the concept onto stochastic setting naturally. For further regularity of solutions, we are able to bound the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>×</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo><mo>)</mo></math></span>-norm of the vorticity and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn><mo>+</mo><mi>δ</mi></mrow></mfrac></mrow></msup><mo>(</mo><mi>Ω</mi><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>×</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span>-norm of the gradient of the vorticity, in case that the initial vorticity is a finite regular signed measure.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111081"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242640","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

The logarithmic Sobolev inequality on non-compact self-shrinkers 非紧化自收缩器上的对数Sobolev不等式

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111085

Guofang Wang , Chao Xia , Xiqiang Zhang

引用次数: 0

Contractive representations of odometer semigroup 里程表半群的压缩表示

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111077

Anindya Ghatak , Narayan Rakshit , Jaydeb Sarkar , Mansi Suryawanshi

{"title":"Contractive representations of odometer semigroup","authors":"Anindya Ghatak , Narayan Rakshit , Jaydeb Sarkar , Mansi Suryawanshi","doi":"10.1016/j.jfa.2025.111077","DOIUrl":"10.1016/j.jfa.2025.111077","url":null,"abstract":"<div><div>Given a natural number <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, the odometer semigroup <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, also known as the adding machine or the Baumslag-Solitar monoid with two generators, is a well-known object in group theory. This paper examines the odometer semigroup in relation to representations of bounded linear operators. We focus on noncommutative operators and prove that contractive representations of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> always admit to nicer representations of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We give a complete description of representations of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> on the Fock space and relate it to the odometer lifting and subrepresentations of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Along the way, we also classify Nica covariant representations of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111077"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221352","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

Product systems arising from Lévy processes 由lsamvy过程产生的产品系统

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111087

Remus Floricel , Peter Wadel

引用次数: 0

Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices Wigner和确定性对角矩阵中自伴随多项式经验谱分布的Stieltjes变换波动

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111083

Serban Belinschi , Mireille Capitaine , Sandrine Dallaporta , Maxime Fevrier

引用次数: 0

Stability of n-solitons for the Camassa-Holm equation Camassa-Holm方程n孤子的稳定性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111084

Ji Li, Honghu Zhang

引用次数: 0

Null-Lagrangians and calibrations for general nonlocal functionals and an application to the viscosity theory 一般非定域泛函的零拉格朗日量和定标及其在粘度理论中的应用

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111086

Xavier Cabré , Iñigo U. Erneta , Juan-Carlos Felipe-Navarro

引用次数: 0

On the global in time existence and uniqueness of solutions to the Boltzmann hierarchy 玻尔兹曼级数解的全局时间存在唯一性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111079

Ioakeim Ampatzoglou , Joseph K. Miller , Nataša Pavlović , Maja Tasković

{"title":"On the global in time existence and uniqueness of solutions to the Boltzmann hierarchy","authors":"Ioakeim Ampatzoglou , Joseph K. Miller , Nataša Pavlović , Maja Tasković","doi":"10.1016/j.jfa.2025.111079","DOIUrl":"10.1016/j.jfa.2025.111079","url":null,"abstract":"<div><div>In this paper we establish the global in time existence and uniqueness of solutions to the Boltzmann hierarchy, a hierarchy of equations instrumental for the rigorous derivation of the Boltzmann equation from many particles. Inspired by available <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-based a-priori estimate for solutions to the Boltzmann equation, we develop the polynomially weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> a-priori bounds for solutions to the Boltzmann hierarchy and handle the factorial growth of the number of terms in the Dyson's series by reorganizing the sum through a combinatorial technique known as the Klainerman-Machedon board game argument. This paper is the first work that exploits such a combinatorial technique in conjunction with an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-based estimate to prove uniqueness of the mild solutions to the Boltzmann hierarchy. Our proof of existence of global in time mild solutions to the Boltzmann hierarchy for admissible initial data is constructive and it employs known global in time solutions to the Boltzmann equation via a Hewitt-Savage type theorem.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111079"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242641","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

Regularity for the fractional p-Laplace equation 分数阶p-拉普拉斯方程的正则性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111078

Verena Bögelein , Frank Duzaar , Naian Liao , Giovanni Molica Bisci , Raffaella Servadei

引用次数: 0