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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
{"title":"The logarithmic Sobolev inequality on non-compact self-shrinkers","authors":"Guofang Wang ,&nbsp;Chao Xia ,&nbsp;Xiqiang Zhang","doi":"10.1016/j.jfa.2025.111085","DOIUrl":"10.1016/j.jfa.2025.111085","url":null,"abstract":"<div><div>In the paper we establish an optimal logarithmic Sobolev inequality for complete, non-compact, properly embedded self-shrinkers in the Euclidean space, which generalizes a recent result of Brendle <span><span>[10]</span></span> for closed self-shrinkers. We first provide a proof for the logarithmic Sobolev inequality in the Euclidean space by using the Alexandrov-Bakelman-Pucci (ABP) method. Then we use this approach to show an optimal logarithmic Sobolev inequality for complete, non-compact, properly embedded self-shrinkers in the Euclidean space, which is a sharp version of the result of Ecker in <span><span>[21]</span></span>. The proof is a noncompact modification of Brendle's proof for closed submanifolds and has a big potential to provide new inequalities in noncompact manifolds.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111085"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221357","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
{"title":"Product systems arising from Lévy processes","authors":"Remus Floricel ,&nbsp;Peter Wadel","doi":"10.1016/j.jfa.2025.111087","DOIUrl":"10.1016/j.jfa.2025.111087","url":null,"abstract":"<div><div>This paper investigates the structure of product systems of Hilbert spaces derived from Banach space-valued Lévy processes. We establish conditions under which these product systems are completely spatial and show that Gaussian Lévy processes with non-degenerate covariance always give rise to product systems of type I. Furthermore, we construct a continuum of non-isomorphic product systems of type <span><math><mi>I</mi><msub><mrow><mi>I</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> from pure jump Lévy processes.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111087"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203355","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
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 ,&nbsp;Narayan Rakshit ,&nbsp;Jaydeb Sarkar ,&nbsp;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
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
{"title":"Stability of n-solitons for the Camassa-Holm equation","authors":"Ji Li,&nbsp;Honghu Zhang","doi":"10.1016/j.jfa.2025.111084","DOIUrl":"10.1016/j.jfa.2025.111084","url":null,"abstract":"<div><div>In this paper, we investigate the stability of <em>n</em>-soliton solutions to the Camassa-Holm (CH) equation. This is achieved by constructing a Lyapunov functional comprised of local independent conservation laws and higher order terms. We first address the issue of non-uniqueness of local conservation laws arising from the recursion operator, and establish the linear representation between two series of local laws generated by the bi-Hamiltonian structure. With the construction of local independent laws, it is then demonstrated that <em>n</em>-solitons actually realize non-isolated constraint minimizers, based on spectral analysis and computation of Wronskain determinant.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111084"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221355","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
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
{"title":"Null-Lagrangians and calibrations for general nonlocal functionals and an application to the viscosity theory","authors":"Xavier Cabré ,&nbsp;Iñigo U. Erneta ,&nbsp;Juan-Carlos Felipe-Navarro","doi":"10.1016/j.jfa.2025.111086","DOIUrl":"10.1016/j.jfa.2025.111086","url":null,"abstract":"<div><div>In this article we build a null-Lagrangian and a calibration for general nonlocal elliptic functionals in the presence of a field of extremals. Thus, our construction assumes the existence of a family of solutions to the Euler-Lagrange equation whose graphs produce a foliation. Then, as a consequence of the calibration, we show the minimality of each leaf in the foliation. Our model case is the energy functional for the fractional Laplacian, for which such a null-Lagrangian was recently discovered by us.</div><div>As a first application of our calibration, we show that monotone solutions to translation invariant nonlocal equations are minimizers. Our second application is somehow surprising, since here “minimality” is assumed instead of being concluded. We will see that the foliation framework is broad enough to provide a proof which establishes that minimizers of nonlocal elliptic functionals are viscosity solutions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111086"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221358","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 weak convergence for a measure related to a class of conformally invariant fully nonlinear operator 一类共形不变全非线性算子测度的弱收敛性
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111080
Xi-Nan Ma , Wangzhe Wu
{"title":"The weak convergence for a measure related to a class of conformally invariant fully nonlinear operator","authors":"Xi-Nan Ma ,&nbsp;Wangzhe Wu","doi":"10.1016/j.jfa.2025.111080","DOIUrl":"10.1016/j.jfa.2025.111080","url":null,"abstract":"<div><div>Trudinger-Wang introduced the notion of k-Hessian measure associated with k-convex functions, not necessarily continuous, and proved the weak continuity of the associated k-Hessian measure with respect to local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> convergence in 1999. In this paper we find a special divergence structure for the <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>-Yamabe operator which is conformally invariant, and prove the weak continuity of the <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>-Yamabe operator with respect to local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> convergence.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111080"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203215","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
An improved multiplier theorem on rank one noncompact symmetric spaces 秩1非紧对称空间上的一个改进乘子定理
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-30 DOI: 10.1016/j.jfa.2025.111082
Błażej Wróbel
{"title":"An improved multiplier theorem on rank one noncompact symmetric spaces","authors":"Błażej Wróbel","doi":"10.1016/j.jfa.2025.111082","DOIUrl":"10.1016/j.jfa.2025.111082","url":null,"abstract":"<div><div>We prove a multiplier theorem on rank one noncompact symmetric spaces which improves aspects of existing results. Namely, we partially drop specific assumptions on the multiplier function such as a Mikhlin-Hörmander condition. This is replaced by a requirement that parts of the multiplier function on the critical <em>p</em> strip give rise to bounded Fourier multipliers.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111082"},"PeriodicalIF":1.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221356","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
Strict comparison and stable rank one 严格比较，稳定排名第一
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-23 DOI: 10.1016/j.jfa.2025.111065
Huaxin Lin
{"title":"Strict comparison and stable rank one","authors":"Huaxin Lin","doi":"10.1016/j.jfa.2025.111065","DOIUrl":"10.1016/j.jfa.2025.111065","url":null,"abstract":"<div><div>Let <em>A</em> be a <em>σ</em>-unital finite simple <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra which has strict comparison property. We show that if the rank map Γ from the Cuntz semigroup to certain lower semicontinuous affine functions is surjective, then <em>A</em> has tracial approximate oscillation zero and stable rank one. Equivalently, if <em>A</em> is a <em>σ</em>-unital finite simple <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra which has an almost unperforated and almost divisible Cuntz semigroup, then <em>A</em> has stable rank one and tracial approximate oscillation zero.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111065"},"PeriodicalIF":1.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196103","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
On steady states for the Vlasov-Schrödinger-Poisson system 关于Vlasov-Schrödinger-Poisson系统的稳态
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-23 DOI: 10.1016/j.jfa.2025.111069
Younghun Hong , Sangdon Jin
{"title":"On steady states for the Vlasov-Schrödinger-Poisson system","authors":"Younghun Hong ,&nbsp;Sangdon Jin","doi":"10.1016/j.jfa.2025.111069","DOIUrl":"10.1016/j.jfa.2025.111069","url":null,"abstract":"<div><div>The Vlasov-Schrödinger-Poisson system is a kinetic-quantum hybrid model describing quasi-lower dimensional electron gases. For this system, we construct a large class of 2D kinetic/1D quantum steady states in a bounded domain as generalized free energy minimizers, and we show their finite subband structure, monotonicity, uniqueness and <em>conditional</em> dynamical stability. Our proof is based on the concentration-compactness principle, but some additional difficulties arise due to lack of compactness originated from the hybrid nature (see <span><span>Remark 1.9</span></span>). To overcome the difficulties, we introduce a 3-step refinement of a minimizing sequence by rearrangement and partial minimization problems, and the coercivity lemma for the free energy (<span><span>Lemma 5.3</span></span>) is crucially employed.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111069"},"PeriodicalIF":1.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138046","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
Large-scale dispersive estimates for acoustic operators: Homogenization meets localization 声学算子的大规模色散估计：均质化满足局域化
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-05-23 DOI: 10.1016/j.jfa.2025.111068
Mitia Duerinckx , Antoine Gloria
{"title":"Large-scale dispersive estimates for acoustic operators: Homogenization meets localization","authors":"Mitia Duerinckx ,&nbsp;Antoine Gloria","doi":"10.1016/j.jfa.2025.111068","DOIUrl":"10.1016/j.jfa.2025.111068","url":null,"abstract":"<div><div>This work relates quantitatively homogenization to Anderson localization for acoustic operators in disordered media. By blending dispersive estimates for homogenized operators and quantitative homogenization of the wave equation, we derive large-scale dispersive estimates for waves in disordered media that we apply to the spreading of low-energy eigenstates. This gives a short and direct proof that the lower spectrum of the acoustic operator is purely absolutely continuous in case of periodic media, and it further provides new lower bounds on the localization length of possible eigenstates in case of quasiperiodic or random media.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111068"},"PeriodicalIF":1.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169797","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
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