Journal of Functional Analysis最新文献

{"title":"Norm convergence rate for multivariate quadratic polynomials of Wigner matrices","authors":"Jacob Fronk ,&nbsp;Torben Krüger ,&nbsp;Yuriy Nemish","doi":"10.1016/j.jfa.2024.110647","DOIUrl":"10.1016/j.jfa.2024.110647","url":null,"abstract":"<div><p>We study Hermitian non-commutative quadratic polynomials of multiple independent Wigner matrices. We prove that, with the exception of some specific reducible cases, the limiting spectral density of the polynomials always has a square root growth at its edges and prove an optimal local law around these edges. Combining these two results, we establish that, as the dimension <em>N</em> of the matrices grows to infinity, the operator norm of such polynomials <em>q</em> converges to a deterministic limit with a rate of convergence of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>. Here, the exponent in the rate of convergence is optimal. For the specific reducible cases, we also provide a classification of all possible edge behaviors.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022123624003355/pdfft?md5=4e27857829ee38213729e119afe883b6&pid=1-s2.0-S0022123624003355-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161642","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}

{"title":"Small perturbations of polytopes","authors":"Christian Kipp","doi":"10.1016/j.jfa.2024.110644","DOIUrl":"10.1016/j.jfa.2024.110644","url":null,"abstract":"<div><p>Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations if the perturbed body is a polytope. As an application, we derive a necessary condition for polytopal maximizers of the isotropic constant.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002212362400332X/pdfft?md5=e462643d71502f41002932b5ab067bea&pid=1-s2.0-S002212362400332X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142151201","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}

{"title":"Locally universal C⁎-algebras with computable presentations","authors":"Alec Fox ,&nbsp;Isaac Goldbring ,&nbsp;Bradd Hart","doi":"10.1016/j.jfa.2024.110652","DOIUrl":"10.1016/j.jfa.2024.110652","url":null,"abstract":"<div><p>The Kirchberg Embedding Problem (KEP) asks if every <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra embeds into an ultrapower of the Cuntz algebra <span><math><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. Motivated by the recent refutation of the Connes Embedding Problem, we establish two computability-theoretic consequences of a positive solution to KEP. Both of our results follow from the a priori weaker assumption that there exists a locally universal <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra with a computable presentation.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172920","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}

{"title":"Random Carleson sequences for the Hardy space on the polydisc and the unit ball","authors":"Nikolaos Chalmoukis ,&nbsp;Alberto Dayan ,&nbsp;Giuseppe Lamberti","doi":"10.1016/j.jfa.2024.110659","DOIUrl":"10.1016/j.jfa.2024.110659","url":null,"abstract":"<div><p>We study the Kolmogorov <span><math><mn>0</mn><mo>−</mo><mn>1</mn></math></span> law for a random sequence with prescribed radii so that it generates a Carleson measure almost surely, both for the Hardy space on the polydisc and the Hardy space on the unit ball, thus providing improved versions of previous results of the first two authors and of a separate result of Massaneda. In the polydisc, the geometry of such sequences is not well understood, so we proceed by studying the random Gramians generated by random sequences, using tools from the theory of random matrices. Another result we prove, and that is of its own relevance, is the <span><math><mn>0</mn><mo>−</mo><mn>1</mn></math></span> law for a random sequence to be partitioned into <em>M</em> separated sequences with respect to the pseudo-hyperbolic distance, which is used also to describe the random sequences that are interpolating for the Bloch space on the unit disc almost surely.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022123624003471/pdfft?md5=002a3ca282e7fe0e69899ce4b770adcb&pid=1-s2.0-S0022123624003471-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161637","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}

{"title":"Weak solutions of anisotropic (and crystalline) inverse mean curvature flow as limits of p-capacitary potentials","authors":"Esther Cabezas-Rivas ,&nbsp;Salvador Moll ,&nbsp;Marcos Solera","doi":"10.1016/j.jfa.2024.110642","DOIUrl":"10.1016/j.jfa.2024.110642","url":null,"abstract":"<div><p>We construct weak solutions of the anisotropic inverse mean curvature flow (A-IMCF) under very mild assumptions both on the anisotropy (which is simply a norm in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> with no ellipticity nor smoothness requirements, in order to include the crystalline case) and on the initial data. By means of an approximation procedure introduced by Moser, our solutions are limits of anisotropic <em>p</em>-harmonic functions or <em>p</em>-capacitary functions (after a change of variable), and we get uniqueness both for the approximating solutions (i.e., uniqueness of <em>p</em>-capacitary functions) and the limiting ones. Our notion of weak solution still recovers variational and geometric definitions similar to those introduced by Huisken-Ilmanen, but requires to work within the broader setting of <em>BV</em>-functions. Despite of this, we still reach classical results like the continuity and exponential growth of perimeter, as well as outward minimizing properties of the sublevel sets. Moreover, by assuming the extra regularity given by an interior rolling ball condition (where a sliding Wulff shape plays the role of a ball), the solutions are shown to be continuous and satisfy Harnack inequalities. Finally, examples of explicit solutions are built.</p></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022123624003306/pdfft?md5=b8aed4f15cb7f0e5872276ff50c4a2cd&pid=1-s2.0-S0022123624003306-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142130089","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}

{"title":"A geometric Elliott invariant and noncommutative rigidity of mapping tori","authors":"Hao Guo ,&nbsp;Valerio Proietti ,&nbsp;Hang Wang","doi":"10.1016/j.jfa.2024.110625","DOIUrl":"10.1016/j.jfa.2024.110625","url":null,"abstract":"<div><p>We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, a leafwise homotopy equivalence of two mapping tori associated to <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>-actions on a compact space can be lifted to an isomorphism of their foliation <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras. This property is a noncommutative analogue of topological rigidity in the context of foliated spaces whose space of leaves is singular, where isomorphism type of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra replaces homeomorphism type. Our technique is to develop a geometric approach to the Elliott invariant that relies on topological and index-theoretic data from the mapping torus. We also discuss how our construction can be extended to slightly more general homotopy quotients arising from actions of discrete cocompact subgroups of simply connected solvable Lie groups, as well as how the theory can be applied to the magnetic gap-labelling problem for certain Cantor minimal systems.</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/S0022123624003136/pdfft?md5=a1cbbfe5bdbc4ef488f7c160f8a48b02&pid=1-s2.0-S0022123624003136-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076533","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}

{"title":"The support of mixed area measures involving a new class of convex bodies","authors":"Daniel Hug ,&nbsp;Paul A. Reichert","doi":"10.1016/j.jfa.2024.110622","DOIUrl":"10.1016/j.jfa.2024.110622","url":null,"abstract":"<div><p>Mixed volumes in <em>n</em>-dimensional Euclidean space are functionals of <em>n</em>-tuples of convex bodies <span><math><mi>K</mi><mo>,</mo><mi>L</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub></math></span>. The Alexandrov–Fenchel inequalities are fundamental inequalities between mixed volumes of convex bodies. As very special cases they cover or imply many important inequalities between basic geometric functionals. A complete characterization of the equality cases in the Alexandrov–Fenchel inequality remains a challenging open problem. Major recent progress was made by Yair Shenfeld and Ramon van Handel <span><span>[13]</span></span>, <span><span>[14]</span></span>, in particular they resolved the problem in the cases where <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub></math></span> are polytopes, zonoids or smooth bodies (under some dimensional restriction). In <span><span>[6]</span></span> we introduced the class of polyoids, which are defined as limits of finite Minkowski sums of polytopes having a bounded number vertices. Polyoids encompass polytopes, zonoids and triangle bodies, and they can be characterized by means of generating measures. Based on this characterization and Shenfeld and van Handel's contribution (and under a dimensional restriction), we extended their result to polyoids (or smooth bodies). Our previous result was stated in terms of the support of the mixed area measure associated with the unit ball <span><math><msup><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub></math></span>. This characterization result is completed in the present work which more generally provides a geometric description of the support of the mixed area measure of an arbitrary <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-tuple of polyoids (or smooth bodies). The result thus (partially) confirms a long-standing conjecture by Rolf Schneider in the case of polyoids, and hence in particular it covers the case of zonoids and triangle bodies.</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/S0022123624003100/pdfft?md5=9ccb46a820f8253bb7bd5d6a8a399a34&pid=1-s2.0-S0022123624003100-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076535","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}

{"title":"A transverse index theorem in the calculus of filtered manifolds","authors":"Clément Cren","doi":"10.1016/j.jfa.2024.110618","DOIUrl":"10.1016/j.jfa.2024.110618","url":null,"abstract":"<div><p>We use filtrations of the tangent bundle of a manifold starting with an integrable subbundle to define transverse symbols to the corresponding foliation, define a condition of transversally Rockland, and prove that transversally Rockland operators yield a K-homology class. We construct an equivariant KK-class for transversally Rockland transverse symbols, and show a Poincaré duality type result linking the class of an operator and its symbol.</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/S0022123624003069/pdfft?md5=f2cc62e9a513ba6e128bb8d1ed87c035&pid=1-s2.0-S0022123624003069-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141992887","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}

{"title":"Functors between Kasparov categories from étale groupoid correspondences","authors":"Alistair Miller","doi":"10.1016/j.jfa.2024.110623","DOIUrl":"10.1016/j.jfa.2024.110623","url":null,"abstract":"<div><p>For an étale correspondence <span><math><mi>Ω</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>H</mi></math></span> of étale groupoids, we construct an induction functor <span><math><msub><mrow><mi>Ind</mi></mrow><mrow><mi>Ω</mi></mrow></msub><mo>:</mo><msup><mrow><mi>KK</mi></mrow><mrow><mi>H</mi></mrow></msup><mo>→</mo><msup><mrow><mi>KK</mi></mrow><mrow><mi>G</mi></mrow></msup></math></span> between equivariant Kasparov categories. We introduce the crossed product of an <em>H</em>-equivariant correspondence by Ω, and use this to build a natural transformation <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>Ω</mi></mrow></msub><mo>:</mo><msub><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>(</mo><mi>G</mi><mo>⋉</mo><msub><mrow><mi>Ind</mi></mrow><mrow><mi>Ω</mi></mrow></msub><mo>−</mo><mo>)</mo><mo>⇒</mo><msub><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>(</mo><mi>H</mi><mo>⋉</mo><mo>−</mo><mo>)</mo></math></span>. When Ω is proper these constructions naturally sit above an induced map in K-theory <span><math><msub><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo><mo>→</mo><msub><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mi>H</mi><mo>)</mo><mo>)</mo></math></span>.</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/S0022123624003112/pdfft?md5=1a5e025b2f1dc2faf5a65e90aee3d000&pid=1-s2.0-S0022123624003112-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142021200","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}

{"title":"On the critical points of solutions of PDE in non-convex settings: The case of concentrating solutions","authors":"F. Gladiali ,&nbsp;M. Grossi","doi":"10.1016/j.jfa.2024.110620","DOIUrl":"10.1016/j.jfa.2024.110620","url":null,"abstract":"<div><p>In this paper we are concerned with the number of critical points of solutions of nonlinear elliptic equations. We will deal with the case of non-convex, contractile and non-contractile planar domains. We will prove results on the estimate of their number as well as their index. In some cases we will provide the exact calculation. The toy problem concerns the multi-peak solutions of the Gel'fand problem, namely<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>λ</mi><msup><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></msup><mspace></mspace></mtd><mtd><mtext> in </mtext><mi>Ω</mi></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace></mtd><mtd><mtext> on </mtext><mo>∂</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is a bounded smooth domain and <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span> is a small parameter.</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":"142021201","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}