Journal of Functional Analysis最新文献_第4页

A Liouville theorem for the Lane-Emden system in the half-space 半空间中Lane-Emden系统的Liouville定理

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111107

Yimei Li , Philippe Souplet

引用次数: 0

Asymptotic behaviour of semigroup traces and Schatten classes of resolvents 解的半群迹和Schatten类的渐近性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111101

Bruno Iochum , Valentin A. Zagrebnov

引用次数: 0

Derivation of renormalized Hartree-Fock-Bogoliubov and quantum Boltzmann equations in an interacting Bose gas 相互作用玻色气体中重整化Hartree-Fock-Bogoliubov方程和量子玻尔兹曼方程的推导

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111096

Thomas Chen , Michael Hott

{"title":"Derivation of renormalized Hartree-Fock-Bogoliubov and quantum Boltzmann equations in an interacting Bose gas","authors":"Thomas Chen , Michael Hott","doi":"10.1016/j.jfa.2025.111096","DOIUrl":"10.1016/j.jfa.2025.111096","url":null,"abstract":"<div><div>Our previous work <span><span>[37]</span></span> presented a rigorous derivation of quantum Boltzmann equations near a Bose-Einstein condensate (BEC). Here, we extend it with a complete characterization of the leading order fluctuation dynamics. For this purpose, we correct the latter via an appropriate Bogoliubov rotation, in partial analogy to the approach by Grillakis-Machedon et al. <span><span>[60]</span></span>, in addition to the Weyl transformation applied in <span><span>[37]</span></span>. Based on the analysis of the third order expansion of the BEC wave function, and the second order expansions of the pair-correlations, we show that through a renormalization strategy, various contributions to the effective Hamiltonian can be iteratively eliminated by an appropriate choice of the Weyl and Bogoliubov transformations. This leads to a separation of renormalized Hartree-Fock-Bogoliubov (HFB) equations and quantum Boltzmann equations. A multitude of terms that were included in the error term in <span><span>[37]</span></span> is now identified as contributions to the HFB renormalization terms. Thereby, the error bound in the work at hand is improved significantly. To the given order, it is now sharp, and matches the order or magnitude expected from scaling considerations. Consequently, we extend the time of validity to <span><math><mi>t</mi><mo>∼</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>N</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> compared to <span><math><mi>t</mi><mo>∼</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>N</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>N</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> before. We expect our approach to be extensible to smaller orders in <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111096"},"PeriodicalIF":1.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338324","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

Solvability for the Ginzburg-Landau equation linearized at the degree-one vortex 一级涡线性化的金兹堡-朗道方程的可解性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111105

Manuel del Pino, Rowan Juneman, Monica Musso

引用次数: 0

Restrictions of pure states to subspaces of C⁎-algebras C -代数的纯态对子空间的限制

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-17 DOI: 10.1016/j.jfa.2025.111104

Raphaël Clouâtre

{"title":"Restrictions of pure states to subspaces of C⁎-algebras","authors":"Raphaël Clouâtre","doi":"10.1016/j.jfa.2025.111104","DOIUrl":"10.1016/j.jfa.2025.111104","url":null,"abstract":"<div><div>Given a unital subspace <em>M</em> of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra <em>B</em>, the fundamental problem that we consider is to describe those pure states <em>ω</em> on <em>B</em> for which <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub><mo>=</mo><mo>{</mo><mi>ω</mi><mo>}</mo></math></span>, where <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span> is the set of states on <em>B</em> extending <span><math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math></span>. In other words, we aim to understand when <span><math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math></span> admits a unique extension to a state on <em>B</em>. We find that the obvious necessary condition that <span><math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math></span> also be pure is sufficient in some naturally occurring examples, but not in general. Guided by classical results for spaces of continuous functions, we then turn to noncommutative peaking phenomena, and to several variations on noncommutative peak points that have previously appeared in the literature. We illustrate that all of them are in fact distinct, address their existence and, in some cases, their relative abundance. To solve our main problem, we introduce a new type of peaking behaviour for <em>ω</em>, namely that the set <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span> be what we call an <em>M</em>-<em>pinnacle set</em>. Roughly speaking, our main result is that <span><math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math></span> admits a unique extension to <em>B</em> if and only if <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span> is an <em>M</em>-pinnacle set.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111104"},"PeriodicalIF":1.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491152","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

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