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(Almost isometric) local retracts in metric spaces (度量空间中的（几乎等距）局部回缩
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-08-13 DOI: 10.1016/j.jfa.2024.110627
Andrés Quilis , Abraham Rueda Zoca
{"title":"(Almost isometric) local retracts in metric spaces","authors":"Andrés Quilis ,&nbsp;Abraham Rueda Zoca","doi":"10.1016/j.jfa.2024.110627","DOIUrl":"10.1016/j.jfa.2024.110627","url":null,"abstract":"<div><p>We introduce the notion of (almost isometric) local retracts in metric space as a natural non-linear version of the concepts of ideals and almost isometric ideals in Banach spaces. We prove that given two metric spaces <span><math><mi>N</mi><mo>⊆</mo><mi>M</mi></math></span> there always exists an almost isometric local retract <span><math><mi>S</mi><mo>⊆</mo><mi>M</mi></math></span> with <span><math><mi>N</mi><mo>⊆</mo><mi>S</mi></math></span> and <span><math><mi>d</mi><mi>e</mi><mi>n</mi><mi>s</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>=</mo><mi>d</mi><mi>e</mi><mi>n</mi><mi>s</mi><mo>(</mo><mi>S</mi><mo>)</mo></math></span>. We also prove that metric spaces which are local retracts (respectively almost isometric local retracts) can be characterised in terms of a condition of extendability of Lipschitz functions (respectively almost isometries) between finite metric spaces. Various examples and counterexamples are exhibited.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002212362400315X/pdfft?md5=12d32ad67a62e301f9eba5c798a10628&pid=1-s2.0-S002212362400315X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142021202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fixed-point formula for Dirac operators on Lie groupoids 列群上狄拉克算子的定点公式
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-08-13 DOI: 10.1016/j.jfa.2024.110624
Ahmad Reza Haj Saeedi Sadegh , Shiqi Liu , Yiannis Loizides , Jesus Sanchez
{"title":"A fixed-point formula for Dirac operators on Lie groupoids","authors":"Ahmad Reza Haj Saeedi Sadegh ,&nbsp;Shiqi Liu ,&nbsp;Yiannis Loizides ,&nbsp;Jesus Sanchez","doi":"10.1016/j.jfa.2024.110624","DOIUrl":"10.1016/j.jfa.2024.110624","url":null,"abstract":"<div><p>We study equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an action of an auxiliary compact Lie group. We use the Getzler rescaling method to derive a fixed-point formula for the pairing of a trace with the K-theory class of such a family. For the pair groupoid of a closed manifold, our formula reduces to the standard fixed-point formula for the equivariant index of a Dirac operator. Further examples involve foliations and manifolds equipped with a normal crossing divisor.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142021034","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
Bauer simplices and the small boundary property 鲍尔简约和小边界特性
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-08-13 DOI: 10.1016/j.jfa.2024.110619
David Kerr, Grigoris Kopsacheilis, Spyridon Petrakos
{"title":"Bauer simplices and the small boundary property","authors":"David Kerr,&nbsp;Grigoris Kopsacheilis,&nbsp;Spyridon Petrakos","doi":"10.1016/j.jfa.2024.110619","DOIUrl":"10.1016/j.jfa.2024.110619","url":null,"abstract":"<div><p>We show that, for every minimal action of a countably infinite discrete group on a compact metrizable space, if the extreme boundary of the simplex of invariant Borel probability measures is closed and has finite covering dimension then the action has the small boundary property.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022123624003070/pdfft?md5=e75e9e687a8f6b2feb4b93beccad17e0&pid=1-s2.0-S0022123624003070-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature 分布非负本征曲率弱规则曲面的凸性
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-08-13 DOI: 10.1016/j.jfa.2024.110616
Mohammad Reza Pakzad
{"title":"Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature","authors":"Mohammad Reza Pakzad","doi":"10.1016/j.jfa.2024.110616","DOIUrl":"10.1016/j.jfa.2024.110616","url":null,"abstract":"<div><p>We prove that the image of an isometric embedding into <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> of a two dimensional complete Riemannian manifold <span><math><mo>(</mo><mi>Σ</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> without boundary is a convex surface, provided that, first, both the embedding and the metric <em>g</em> enjoy a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> regularity for some <span><math><mi>α</mi><mo>&gt;</mo><mn>2</mn><mo>/</mo><mn>3</mn></math></span>, and second, the distributional Gaussian curvature of <em>g</em> is nonnegative and nonzero. The analysis must pass through some key observations regarding solutions to the very weak Monge-Ampère equation.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076536","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
Well-posedness of the stationary and slowly traveling wave problems for the free boundary incompressible Navier-Stokes equations 自由边界不可压缩纳维-斯托克斯方程的静止波和慢行波问题的良好拟合
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-08-13 DOI: 10.1016/j.jfa.2024.110617
Noah Stevenson , Ian Tice
{"title":"Well-posedness of the stationary and slowly traveling wave problems for the free boundary incompressible Navier-Stokes equations","authors":"Noah Stevenson ,&nbsp;Ian Tice","doi":"10.1016/j.jfa.2024.110617","DOIUrl":"10.1016/j.jfa.2024.110617","url":null,"abstract":"<div><p>We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a general phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The setting of our result is a horizontally-infinite fluid of finite depth with a flat, rigid bottom and a free boundary top. A constant gravitational field acts normal to bottom, and the free boundary experiences surface tension. In addition to these gravity-capillary effects, we allow for applied stress tensors to act on the free surface region and applied forces to act in the bulk. These are posited to be in either stationary or traveling form.</p><p>In the absence of any applied stress or force, the system reverts to a quiescent equilibrium; in contrast, when such sources of stress or force are present, stationary or traveling waves are generated. We develop a small data well-posedness theory for this problem by proving that there exists a neighborhood of the origin in stress, force, and wave speed data-space in which we obtain the existence and uniqueness of stationary and traveling wave solutions that depend continuously on the stress-force data, wave speed, and other physical parameters. To the best of our knowledge, this is the first proof of well-posedness of the solitary stationary wave problem and the first continuous embedding of the stationary wave problem into the traveling wave problem. Our techniques are based on vector-valued harmonic analysis, a novel method of indirect symbol calculus, and the implicit function theorem.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142007039","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
Γ-convergence of the Ginzburg-Landau functional with tangential boundary conditions 具有切向边界条件的金兹堡-兰道函数的Γ-收敛性
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-08-13 DOI: 10.1016/j.jfa.2024.110621
Stan Alama, Lia Bronsard, Andrew Colinet
{"title":"Γ-convergence of the Ginzburg-Landau functional with tangential boundary conditions","authors":"Stan Alama,&nbsp;Lia Bronsard,&nbsp;Andrew Colinet","doi":"10.1016/j.jfa.2024.110621","DOIUrl":"10.1016/j.jfa.2024.110621","url":null,"abstract":"<div><p>A classical result in the study of Ginzburg-Landau equations is that, for Dirichlet or Neumann boundary conditions, if a sequence of functions has energy uniformly bounded on a logarithmic scale then we can find a subsequence whose Jacobians are convergent in suitable dual spaces and whose renormalized energy is at least the sum of absolute degrees of vortices. However, the corresponding question for the case of tangential or normal boundary conditions has not been considered. In addition, the question of convergence of up to the boundary is not very well understood. Here, we consider these questions for a bounded, connected, open set of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> boundary.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142011342","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
Descent modulus and applications 下降模量和应用
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-08-13 DOI: 10.1016/j.jfa.2024.110626
Aris Daniilidis , Laurent Miclo , David Salas
{"title":"Descent modulus and applications","authors":"Aris Daniilidis ,&nbsp;Laurent Miclo ,&nbsp;David Salas","doi":"10.1016/j.jfa.2024.110626","DOIUrl":"10.1016/j.jfa.2024.110626","url":null,"abstract":"<div><p>The norm of the gradient <span><math><mo>‖</mo><mi>∇</mi><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>‖</mo></math></span> measures the maximum descent of a real-valued smooth function <em>f</em> at <em>x</em>. For (nonsmooth) convex functions, this is expressed by the distance <span><math><mrow><mi>dist</mi></mrow><mo>(</mo><mn>0</mn><mo>,</mo><mo>∂</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></span> of the subdifferential to the origin, while for general real-valued functions defined on metric spaces by the notion of metric slope <span><math><mo>|</mo><mi>∇</mi><mi>f</mi><mo>|</mo><mo>(</mo><mi>x</mi><mo>)</mo></math></span>. In this work we propose an axiomatic definition of descent modulus <span><math><mi>T</mi><mo>[</mo><mi>f</mi><mo>]</mo><mo>(</mo><mi>x</mi><mo>)</mo></math></span> of a real-valued function <em>f</em> at every point <em>x</em>, defined on a general (not necessarily metric) space. The definition encompasses all above instances as well as average descents for functions defined on probability spaces. We show that a large class of functions are completely determined by their descent modulus and corresponding critical values. This result is already surprising in the smooth case: a one-dimensional information (norm of the gradient) turns out to be almost as powerful as the knowledge of the full gradient mapping. In the nonsmooth case, the key element for this determination result is the break of symmetry induced by a downhill orientation, in the spirit of the definition of the metric slope. The particular case of functions defined on finite spaces is studied in the last section. In this case, we obtain an explicit classification of descent operators that are, in some sense, typical.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022123624003148/pdfft?md5=c3c69cd4d272de9fe328368006f32de8&pid=1-s2.0-S0022123624003148-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142040953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Gauss Image Problem with weak Aleksandrov condition 弱阿列克桑德罗夫条件下的高斯图像问题
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-07-31 DOI: 10.1016/j.jfa.2024.110611
Vadim Semenov
{"title":"The Gauss Image Problem with weak Aleksandrov condition","authors":"Vadim Semenov","doi":"10.1016/j.jfa.2024.110611","DOIUrl":"10.1016/j.jfa.2024.110611","url":null,"abstract":"<div><p>We introduce a relaxation of the Aleksandrov condition for the Gauss Image Problem. This weaker condition turns out to be a necessary condition for two measures to be related by a convex body. We provide several properties of the new condition. A solution to the Gauss Image Problem is obtained for the case when one of the measures is assumed to be discrete and the another measure is assumed to be absolutely continuous, under the new relaxed assumption.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142048589","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
Strichartz estimates for the Schrödinger equation on negatively curved compact manifolds 负弯曲紧凑流形上薛定谔方程的斯特里查兹估计值
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-07-31 DOI: 10.1016/j.jfa.2024.110613
Matthew D. Blair , Xiaoqi Huang , Christopher D. Sogge
{"title":"Strichartz estimates for the Schrödinger equation on negatively curved compact manifolds","authors":"Matthew D. Blair ,&nbsp;Xiaoqi Huang ,&nbsp;Christopher D. Sogge","doi":"10.1016/j.jfa.2024.110613","DOIUrl":"10.1016/j.jfa.2024.110613","url":null,"abstract":"<div><p>We obtain improved Strichartz estimates for solutions of the Schrödinger equation on negatively curved compact manifolds which improve the classical universal results of Burq, Gérard and Tzvetkov <span><span>[11]</span></span> in this geometry. In the case where the spatial manifold is a hyperbolic surface we are able to obtain no-loss <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>t</mi><mo>,</mo><mi>x</mi></mrow><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></msubsup></math></span>-estimates on intervals of length <span><math><mi>log</mi><mo>⁡</mo><mi>λ</mi><mo>⋅</mo><msup><mrow><mi>λ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> for initial data whose frequencies are comparable to <em>λ</em>, which, given the role of the Ehrenfest time, is the natural analog of the universal results in <span><span>[11]</span></span>. We also obtain improved endpoint Strichartz estimates for manifolds of nonpositive curvature, which cannot hold for spheres.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948993","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
Differential operators on C⁎-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid C⁎玻上的微分算子及其在切线群上的平滑函数微积分和施瓦茨函数中的应用
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2024-07-31 DOI: 10.1016/j.jfa.2024.110615
Omar Mohsen
{"title":"Differential operators on C⁎-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid","authors":"Omar Mohsen","doi":"10.1016/j.jfa.2024.110615","DOIUrl":"10.1016/j.jfa.2024.110615","url":null,"abstract":"<div><p>We introduce the notion of a differential operator on <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras. This is a noncommutative analogue of a differential operator on a smooth manifold. We show that the common closed domain of all differential operators is closed under smooth functional calculus. As a corollary, we show that Schwartz functions on Connes tangent groupoid are closed under smooth functional calculus.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948891","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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