Pub Date : 2025-12-23DOI: 10.1016/j.jfa.2025.111320
Alexander Elgart , Abel Klein
It is shown that the infinite random Heisenberg XXZ spin- chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of the parameter space. This region depends only on the energy interval and includes weak interaction and strong disorder regimes. The crucial step in the argument is a proof that if the Green functions for the associated finite systems Hamiltonians exhibit certain (volume-dependent) decay properties in a fixed energy interval, then the infinite volume Green function decays in the same interval as well. The pertinent finite systems decay properties for the random XXZ spin chain had been previously verified by the authors.
{"title":"Localization phenomena in the random XXZ spin chain","authors":"Alexander Elgart , Abel Klein","doi":"10.1016/j.jfa.2025.111320","DOIUrl":"10.1016/j.jfa.2025.111320","url":null,"abstract":"<div><div>It is shown that the infinite random Heisenberg XXZ spin-<span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of the parameter space. This region depends only on the energy interval and includes weak interaction and strong disorder regimes. The crucial step in the argument is a proof that if the Green functions for the associated finite systems Hamiltonians exhibit certain (volume-dependent) decay properties in a fixed energy interval, then the infinite volume Green function decays in the same interval as well. The pertinent finite systems decay properties for the random XXZ spin chain had been previously verified by the authors.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111320"},"PeriodicalIF":1.6,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882832","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}
Pub Date : 2025-12-22DOI: 10.1016/j.jfa.2025.111321
Anh Xuan Do , Nguyen Lam , Guozhen Lu
Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and upper bounds for the sharp stability constants and compute their exact limits when the dimension . Our proofs rely on spherical harmonics decomposition and Fourier analysis, differing significantly from existing approaches in the literature. Our results substantially improve the stability constants of the second order Heisenberg Uncertainty Principle recently obtained in [27]. As direct consequences of our main results, we also establish the sharp stability, with exact asymptotic behavior of the stability constants, of the Heisenberg Uncertainty Principle with curl-free vector fields and a sharp version of the second order Poincaré type inequality with Gaussian measure.
{"title":"Sharp stability of the Heisenberg Uncertainty Principle: Second-order and curl-free field cases","authors":"Anh Xuan Do , Nguyen Lam , Guozhen Lu","doi":"10.1016/j.jfa.2025.111321","DOIUrl":"10.1016/j.jfa.2025.111321","url":null,"abstract":"<div><div>Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and upper bounds for the sharp stability constants and compute their exact limits when the dimension <span><math><mi>N</mi><mo>→</mo><mo>∞</mo></math></span>. Our proofs rely on spherical harmonics decomposition and Fourier analysis, differing significantly from existing approaches in the literature. Our results substantially improve the stability constants of the second order Heisenberg Uncertainty Principle recently obtained in <span><span>[27]</span></span>. As direct consequences of our main results, we also establish the sharp stability, with exact asymptotic behavior of the stability constants, of the Heisenberg Uncertainty Principle with curl-free vector fields and a sharp version of the second order Poincaré type inequality with Gaussian measure.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111321"},"PeriodicalIF":1.6,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882829","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}
Pub Date : 2025-12-19DOI: 10.1016/j.jfa.2025.111316
Jordy Timo van Velthoven , Felix Voigtlaender
We provide a characterization of two expansive dilation matrices yielding equal discrete anisotropic Triebel-Lizorkin spaces. For two such matrices A and B, and arbitrary and , it is shown that if and only if the set is finite, or in the trivial case when and . This provides an extension of a result by Triebel for diagonal dilations to arbitrary expansive matrices. The obtained classification of dilations is different from corresponding results for anisotropic Triebel-Lizorkin function spaces.
{"title":"Discrete Triebel-Lizorkin spaces and expansive matrices","authors":"Jordy Timo van Velthoven , Felix Voigtlaender","doi":"10.1016/j.jfa.2025.111316","DOIUrl":"10.1016/j.jfa.2025.111316","url":null,"abstract":"<div><div>We provide a characterization of two expansive dilation matrices yielding equal discrete anisotropic Triebel-Lizorkin spaces. For two such matrices <em>A</em> and <em>B</em>, and arbitrary <span><math><mi>α</mi><mo>∈</mo><mi>R</mi></math></span> and <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span>, it is shown that <span><math><msubsup><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mo>(</mo><mi>B</mi><mo>)</mo></math></span> if and only if the set <span><math><mo>{</mo><msup><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow></msup><msup><mrow><mi>B</mi></mrow><mrow><mo>−</mo><mi>j</mi></mrow></msup><mo>:</mo><mi>j</mi><mo>∈</mo><mi>Z</mi><mo>}</mo></math></span> is finite, or in the trivial case when <span><math><mo>|</mo><mi>det</mi><mo></mo><mo>(</mo><mi>A</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>p</mi></mrow></msup><mo>=</mo><mo>|</mo><mi>det</mi><mo></mo><mo>(</mo><mi>B</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>p</mi></mrow></msup></math></span> and <span><math><mi>p</mi><mo>=</mo><mi>q</mi></math></span>. This provides an extension of a result by Triebel for diagonal dilations to arbitrary expansive matrices. The obtained classification of dilations is different from corresponding results for anisotropic Triebel-Lizorkin function spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111316"},"PeriodicalIF":1.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882830","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}
Pub Date : 2025-12-19DOI: 10.1016/j.jfa.2025.111315
Yu Gu, Ran Tao
We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. Utilizing this identity, we obtain estimates for the polymer endpoints, leading to optimal fluctuation exponents for the height function in both the subcritical and critical regimes, as well as an optimal upper bound for the fluctuation exponents in the extended critical regime. We also compute the average growth rate as a function of the boundary parameter.
{"title":"Fluctuation exponents of the half-space KPZ at stationarity","authors":"Yu Gu, Ran Tao","doi":"10.1016/j.jfa.2025.111315","DOIUrl":"10.1016/j.jfa.2025.111315","url":null,"abstract":"<div><div>We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. Utilizing this identity, we obtain estimates for the polymer endpoints, leading to optimal fluctuation exponents for the height function in both the subcritical and critical regimes, as well as an optimal upper bound for the fluctuation exponents in the extended critical regime. We also compute the average growth rate as a function of the boundary parameter.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111315"},"PeriodicalIF":1.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845558","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}
Pub Date : 2025-12-19DOI: 10.1016/j.jfa.2025.111322
Lorenz Frühwirth, Joscha Prochno
In this article, we present a precise deviation formula for the intersection of two Orlicz balls generated by Orlicz functions V and W. Additionally, we establish a (quantitative) central limit theorem in the critical case and a strong law of large numbers for the “W-norm” of the uniform distribution on . Our techniques also enable us to derive a precise formula for the thin-shell concentration of uniformly distributed random vectors in high-dimensional Orlicz balls. In our approach we establish an Edgeworth-expansion using methods from harmonic analysis together with an exponential change of measure argument.
{"title":"Sharp concentration phenomena in high-dimensional Orlicz balls","authors":"Lorenz Frühwirth, Joscha Prochno","doi":"10.1016/j.jfa.2025.111322","DOIUrl":"10.1016/j.jfa.2025.111322","url":null,"abstract":"<div><div>In this article, we present a precise deviation formula for the intersection of two Orlicz balls generated by Orlicz functions <em>V</em> and <em>W</em>. Additionally, we establish a (quantitative) central limit theorem in the critical case and a strong law of large numbers for the “<em>W</em>-norm” of the uniform distribution on <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>V</mi><mo>)</mo></mrow></msup></math></span>. Our techniques also enable us to derive a precise formula for the thin-shell concentration of uniformly distributed random vectors in high-dimensional Orlicz balls. In our approach we establish an Edgeworth-expansion using methods from harmonic analysis together with an exponential change of measure argument.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111322"},"PeriodicalIF":1.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880794","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}
We present an existence and uniqueness result for weak solutions of Dirichlet boundary value problems governed by a nonlocal operator in divergence form and in the presence of a datum which is assumed to belong only to and to be suitably dominated.
We also prove that the solution that we find converges, as , to a solution of the local counterpart problem, recovering the classical result as a limit case. This requires some nontrivial customized uniform estimates and representation formulas, given that the datum is only in and therefore the usual regularity theory cannot be leveraged to our benefit in this framework.
The limit process uses a nonlocal operator, obtained as an affine transformation of a homogeneous kernel, which recovers, in the limit as , every classical operator in divergence form.
{"title":"Nonlocal operators in divergence form and existence theory for integrable data","authors":"David Arcoya , Serena Dipierro , Edoardo Proietti Lippi , Caterina Sportelli , Enrico Valdinoci","doi":"10.1016/j.jfa.2025.111317","DOIUrl":"10.1016/j.jfa.2025.111317","url":null,"abstract":"<div><div>We present an existence and uniqueness result for weak solutions of Dirichlet boundary value problems governed by a nonlocal operator in divergence form and in the presence of a datum which is assumed to belong only to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> and to be suitably dominated.</div><div>We also prove that the solution that we find converges, as <span><math><mi>s</mi><mo>↗</mo><mn>1</mn></math></span>, to a solution of the local counterpart problem, recovering the classical result as a limit case. This requires some nontrivial customized uniform estimates and representation formulas, given that the datum is only in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> and therefore the usual regularity theory cannot be leveraged to our benefit in this framework.</div><div>The limit process uses a nonlocal operator, obtained as an affine transformation of a homogeneous kernel, which recovers, in the limit as <span><math><mi>s</mi><mo>↗</mo><mn>1</mn></math></span>, every classical operator in divergence form.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111317"},"PeriodicalIF":1.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882831","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}
This paper studies the relations between extendability of different classes of Sobolev and BV functions from closed sets in general metric measure spaces. Under the assumption that the metric measure space satisfies a weak -Poincaré inequality and measure doubling, we prove further properties for the extension sets. In the case of the Euclidean plane, we show that compact finitely connected BV-extension sets are always also -extension sets. This is shown via a local quasiconvexity result for the complement of the extension set.
{"title":"Closed BV-extension and W1,1-extension sets","authors":"Emanuele Caputo , Jesse Koivu , Danka Lučić , Tapio Rajala","doi":"10.1016/j.jfa.2025.111319","DOIUrl":"10.1016/j.jfa.2025.111319","url":null,"abstract":"<div><div>This paper studies the relations between extendability of different classes of Sobolev <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> and <em>BV</em> functions from closed sets in general metric measure spaces. Under the assumption that the metric measure space satisfies a weak <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-Poincaré inequality and measure doubling, we prove further properties for the extension sets. In the case of the Euclidean plane, we show that compact finitely connected <em>BV</em>-extension sets are always also <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>-extension sets. This is shown via a local quasiconvexity result for the complement of the extension set.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111319"},"PeriodicalIF":1.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882890","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":"Schauder frames of discrete translates in L2(R)","authors":"Nir Lev , Anton Tselishchev","doi":"10.1016/j.jfa.2025.111318","DOIUrl":"10.1016/j.jfa.2025.111318","url":null,"abstract":"<div><div>We construct a uniformly discrete sequence <span><math><mo>{</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo><</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo><</mo><mo>⋯</mo><mo>}</mo><mo>⊂</mo><mi>R</mi></math></span> and functions <em>g</em> and <span><math><mo>{</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>}</mo></math></span> in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>, such that every <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> admits a series expansion<span><span><span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></munderover><mo>〈</mo><mi>f</mi><mo>,</mo><msubsup><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>〉</mo><mspace></mspace><mi>g</mi><mo>(</mo><mi>x</mi><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span></span></span> convergent in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> norm.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111318"},"PeriodicalIF":1.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845559","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}
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