Journal of Functional Analysis最新文献

{"title":"On some intrinsic differentiability properties for absolutely continuous functions between Carnot groups and the area formula","authors":"Andrea Pinamonti,&nbsp;Francesco Serra Cassano,&nbsp;Kilian Zambanini","doi":"10.1016/j.jfa.2025.110948","DOIUrl":"10.1016/j.jfa.2025.110948","url":null,"abstract":"<div><div>We discuss <em>Q</em>-absolutely continuous functions between Carnot groups, following Malý's definition for maps of several variables (<span><span>[43]</span></span>). Such maps enjoy nice regularity properties, like continuity, Pansu differentiability a.e., weak differentiability and an area formula. Furthermore, we extend Stein's result concerning the sharp condition for continuity and differentiability a.e. of a Sobolev map in terms of the integrability of the weak gradient: more precisely, we prove that a Sobolev map between Carnot groups with horizontal gradient of its sections uniformly bounded in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>Q</mi><mo>,</mo><mn>1</mn></mrow></msup></math></span> admits a representative which is <em>Q</em>-absolutely continuous.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110948"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685944","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":"Potential theory of Dirichlet forms with jump kernels blowing up at the boundary","authors":"Panki Kim ,&nbsp;Renming Song ,&nbsp;Zoran Vondraček","doi":"10.1016/j.jfa.2025.110934","DOIUrl":"10.1016/j.jfa.2025.110934","url":null,"abstract":"<div><div>In this paper we study the potential theory of Dirichlet forms on the half-space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>d</mi></mrow></msubsup></math></span> defined by the jump kernel <span><math><mi>J</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>=</mo><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mi>d</mi><mo>−</mo><mi>α</mi></mrow></msup><mi>B</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> and the killing potential <span><math><mi>κ</mi><msubsup><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msubsup></math></span>, where <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and <span><math><mi>B</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> can blow up to infinity at the boundary. The jump kernel and the killing potential depend on several parameters. For all admissible values of the parameters involved and all <span><math><mi>d</mi><mo>≥</mo><mn>1</mn></math></span>, we prove that the boundary Harnack principle holds, and establish sharp two-sided estimates on the Green functions of these processes.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110934"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759330","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":"Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature","authors":"Gioacchino Antonelli ,&nbsp;Marco Pozzetta","doi":"10.1016/j.jfa.2025.110940","DOIUrl":"10.1016/j.jfa.2025.110940","url":null,"abstract":"<div><div>In this paper we consider nonnegatively curved finite dimensional Alexandrov spaces with a non-collapsing condition, i.e., such that unit balls have volumes uniformly bounded from below away from zero. We study the relation between the isoperimetric profile, the existence of isoperimetric sets, and the asymptotic structure at infinity of such spaces.</div><div>In this setting, we prove that the following conditions are equivalent: the space has linear volume growth; it is Gromov–Hausdorff asymptotic to one cylinder at infinity; it has uniformly bounded isoperimetric profile; the entire space is a tubular neighborhood of either a line or a ray.</div><div>Moreover, on a space satisfying any of the previous conditions, we prove existence of isoperimetric sets for sufficiently large volumes, and we characterize the geometric rigidity at the level of the isoperimetric profile.</div><div>Specializing our study to the 2-dimensional case, we prove that unit balls have always volumes uniformly bounded from below away from zero, and we prove existence of isoperimetric sets for every volume, characterizing also their topology when the space has no boundary.</div><div>The proofs exploit a variational approach, and in particular apply to Riemannian manifolds with nonnegative sectional curvature and to Euclidean convex bodies. Up to the authors' knowledge, most of the results are new even in these smooth cases.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110940"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737988","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":"Diagonals of self-adjoint operators I: Compact operators","authors":"Marcin Bownik ,&nbsp;John Jasper","doi":"10.1016/j.jfa.2025.110939","DOIUrl":"10.1016/j.jfa.2025.110939","url":null,"abstract":"<div><div>Given a self-adjoint operator <em>T</em> on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> of all possible diagonals of <em>T</em>. For compact operators <em>T</em>, we give a complete characterization of diagonals modulo the kernel of <em>T</em>. That is, we characterize <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> for the class of operators sharing the same nonzero eigenvalues (with multiplicities) as <em>T</em>. Moreover, we determine <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> for a fixed compact operator <em>T</em>, modulo the kernel problem for positive compact operators with finite-dimensional kernel.</div><div>Our results generalize a characterization of diagonals of trace class positive operators by Arveson and Kadison <span><span>[5]</span></span> and diagonals of compact positive operators by Kaftal and Weiss <span><span>[24]</span></span> and Loreaux and Weiss <span><span>[28]</span></span>. The proof uses the technique of diagonal-to-diagonal results, which was pioneered in the earlier joint work of the authors with Siudeja <span><span>[12]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110939"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738470","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":"Degenerate Kirchhoff problems with nonlinear Neumann boundary condition","authors":"Franziska Borer ,&nbsp;Marcos T.O. Pimenta ,&nbsp;Patrick Winkert","doi":"10.1016/j.jfa.2025.110933","DOIUrl":"10.1016/j.jfa.2025.110933","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper we consider degenerate Kirchhoff-type equations of the form&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ξ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;in &lt;/mtext&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ξ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;on &lt;/mtext&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, is a bounded domain with Lipschitz boundary ∂Ω, &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; denotes the double phase operator given by&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;div&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the outer unit normal of Ω at &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;Ξ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110933"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768202","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":"Murray–von Neumann dimension for strictly semifinite weights","authors":"Aldo Garcia Guinto,&nbsp;Matthew Lorentz,&nbsp;Brent Nelson","doi":"10.1016/j.jfa.2025.110938","DOIUrl":"10.1016/j.jfa.2025.110938","url":null,"abstract":"<div><div>Given a von Neumann algebra <em>M</em> equipped with a faithful normal strictly semifinite weight <em>φ</em>, we develop a notion of Murray–von Neumann dimension over <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>φ</mi><mo>)</mo></math></span> that is defined for modules over the basic construction associated to the inclusion <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>φ</mi></mrow></msup><mo>⊂</mo><mi>M</mi></math></span>. For <span><math><mi>φ</mi><mo>=</mo><mi>τ</mi></math></span> a faithful normal tracial state, this recovers the usual Murray–von Neumann dimension for finite von Neumann algebras. If <em>M</em> is either a type <span><math><msub><mrow><mi>III</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> factor with <span><math><mn>0</mn><mo>&lt;</mo><mi>λ</mi><mo>&lt;</mo><mn>1</mn></math></span> or a full type <span><math><msub><mrow><mi>III</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> factor with <span><math><mi>Sd</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>≠</mo><mi>R</mi></math></span>, then amongst extremal almost periodic weights the dimension function depends on <em>φ</em> only up to scaling. As an application, we show that if an inclusion of diffuse factors with separable preduals <span><math><mi>N</mi><mo>⊂</mo><mi>M</mi></math></span> is with expectation <span><math><mi>E</mi></math></span> and admits a compatible extremal almost periodic state <em>φ</em>, then this dimension quantity bounds the index <span><math><mi>Ind</mi><mspace></mspace><mi>E</mi></math></span>, and in fact equals it when the modular operators <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>φ</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>N</mi></mrow></msub></mrow></msub></math></span> have the same point spectrum. In the pursuit of this result, we also show such inclusions always admit Pimsner–Popa orthogonal bases.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110938"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738469","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":"A generating operator for Rankin–Cohen brackets","authors":"Toshiyuki Kobayashi ,&nbsp;Michael Pevzner","doi":"10.1016/j.jfa.2025.110944","DOIUrl":"10.1016/j.jfa.2025.110944","url":null,"abstract":"<div><div>Motivated by the classical ideas of generating functions for orthogonal polynomials, we initiate a new line of investigation on “generating operators” for a family of differential operators between two manifolds. We prove a novel formula of the generating operators for the Rankin–Cohen brackets by using higher-dimensional residue calculus. Various results on the generating operators are also explored from the perspective of infinite-dimensional representation theory.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110944"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785830","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 concept of mapped coercivity for nonlinear operators in Banach spaces","authors":"Roland Becker ,&nbsp;Malte Braack","doi":"10.1016/j.jfa.2025.110893","DOIUrl":"10.1016/j.jfa.2025.110893","url":null,"abstract":"<div><div>We provide a concise proof of existence of the solutions to nonlinear operator equations in separable Banach spaces, without assuming the operator to be monotone. Instead, our main hypotheses consist of a continuity assumption and a mapped coercivity property, which is a generalization of the usual coercivity property for nonlinear operators. In the case of linear operators, we recover the traditional inf-sup condition. To illustrate the applicability of this general concept, we apply it to semi-linear elliptic problems and the Navier-Stokes equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110893"},"PeriodicalIF":1.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620534","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 new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system","authors":"Timothée Crin-Barat ,&nbsp;Yue-Jun Peng ,&nbsp;Ling-Yun Shou ,&nbsp;Jiang Xu","doi":"10.1016/j.jfa.2025.110918","DOIUrl":"10.1016/j.jfa.2025.110918","url":null,"abstract":"<div><div>We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we establish the global well-posedness of classical solutions near constant equilibrium in a critical regularity setting, uniformly with respect to the relaxation parameter <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span>. Then, we introduce an effective unknown motivated by Darcy's law to derive quantitative error estimates at the rate <span><math><mi>O</mi><mo>(</mo><mi>ε</mi><mo>)</mo></math></span> between the rescaled Euler-Maxwell system and the limiting drift-diffusion model. This provides the first global-in-time strong convergence result for the relaxation procedure in the case of ill-prepared data so far.</div><div>We propose a new characterization of the dissipation structure for the non-symmetric relaxation of linearized Euler-Maxwell system, which partitions the frequency space into three distinct regimes (low, medium and high frequencies) associated with different behaviors of the solution. Within each regime, the application of Lyapunov functionals based on the hypocoercivity theory reveals the expected dissipative properties. Moreover, two correction functions are employed to take care of the initial layers in the relaxation convergence.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 2","pages":"Article 110918"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601522","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":"Convergences of combinatorial Ricci flows to degenerated circle packings in hyperbolic background geometry","authors":"Guangming Hu ,&nbsp;Sicheng Lu ,&nbsp;Dong Tan ,&nbsp;Youliang Zhong ,&nbsp;Puchun Zhou","doi":"10.1016/j.jfa.2025.110921","DOIUrl":"10.1016/j.jfa.2025.110921","url":null,"abstract":"<div><div>This paper investigates a kind of degenerated circle packings in hyperbolic background geometry. A main problem is whether a prescribed total geodesic curvature data can be realized by a degenerated circle packing or not. We fully characterize the sufficient and necessary conditions and show the uniqueness. Furthermore, we introduce the combinatorial Ricci flow to find the desired degenerated circle packed surface, analogous to the methods of Chow-Luo <span><span>[7]</span></span> and Takatsu <span><span>[37]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110921"},"PeriodicalIF":1.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620533","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}