Journal of Functional Analysis最新文献

{"title":"Corrigendum to: “Quantization and the resolvent algebra” [J. Funct. Anal. 277 (8) (2019) 2815–2838]","authors":"Teun D.H. van Nuland,&nbsp;Lorenzo Pettinari","doi":"10.1016/j.jfa.2025.111184","DOIUrl":"10.1016/j.jfa.2025.111184","url":null,"abstract":"<div><div>In <span><span>[3]</span></span> it is claimed incorrectly that the Berezin quantization map maps surjectively to the resolvent algebra.<span><span>¹</span></span> We show here that it does not. Similarly, the Berezin map defined on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></math></span> does not reach all compact operators, contrary to what is claimed in <span><span>[2, II.(2.73)]</span></span>.<span><span>²</span></span> We moreover fill a gap in the proof of injectivity of the Berezin quantization map on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of <span><span>[3]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111184"},"PeriodicalIF":1.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933790","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":"Optimal decay of eigenvector overlap for non-Hermitian random matrices","authors":"Giorgio Cipolloni ,&nbsp;László Erdős ,&nbsp;Yuanyuan Xu","doi":"10.1016/j.jfa.2025.111180","DOIUrl":"10.1016/j.jfa.2025.111180","url":null,"abstract":"<div><div>We consider the standard overlap <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>:</mo><mo>=</mo><mo>〈</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>,</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>〉</mo><mo>〈</mo><msub><mrow><mi>l</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>,</mo><msub><mrow><mi>l</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>〉</mo></math></span> of any bi-orthogonal family of left and right eigenvectors of a large random matrix <em>X</em> with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach <span><span>[15]</span></span>, as well as Benaych-Georges and Zeitouni <span><span>[13]</span></span>, to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of <em>X</em> uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111180"},"PeriodicalIF":1.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020130","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":"Lp-integrability of functions with Fourier supports on fractal sets on the moment curve","authors":"Shengze Duan ,&nbsp;Minh-Quy Pham ,&nbsp;Donggeun Ryou","doi":"10.1016/j.jfa.2025.111185","DOIUrl":"10.1016/j.jfa.2025.111185","url":null,"abstract":"<div><div>For <span><math><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mn>1</mn></math></span>, let <em>E</em> be a compact subset of the <em>d</em>-dimensional moment curve in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> such that <span><math><mi>N</mi><mo>(</mo><mi>E</mi><mo>,</mo><mi>ε</mi><mo>)</mo><mo>≲</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup></math></span> for <span><math><mn>0</mn><mo>&lt;</mo><mi>ε</mi><mo>&lt;</mo><mn>1</mn></math></span> where <span><math><mi>N</mi><mo>(</mo><mi>E</mi><mo>,</mo><mi>ε</mi><mo>)</mo></math></span> is the smallest number of <em>ε</em>-balls needed to cover <em>E</em>. We proved that if <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> with<span><span><span><math><mrow><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>:</mo><mo>=</mo><mrow><mo>{</mo><mtable><mtr><mtd><mfrac><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>+</mo><mn>2</mn><mi>α</mi></mrow><mrow><mn>2</mn><mi>α</mi></mrow></mfrac></mtd><mtd><mi>d</mi><mo>≥</mo><mn>3</mn><mo>,</mo></mtd></mtr><mtr><mtd><mfrac><mrow><mn>4</mn></mrow><mrow><mi>α</mi></mrow></mfrac></mtd><mtd><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo></mtd></mtr></mtable></mrow></mrow></math></span></span></span> and <span><math><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is supported on the set <em>E</em>, then <em>f</em> is identically zero. We also proved that the range of <em>p</em> is optimal by considering random Cantor sets on the moment curve. We extended the result of Guo, Iosevich, Zhang and Zorin-Kranich <span><span>[11]</span></span>, including the endpoint. We also considered applications of our results to the failure of the restriction estimates and Wiener Tauberian Theorem.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111185"},"PeriodicalIF":1.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010268","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":"The homotopy type of the linear group of Lebesgue–Bochner and Besov spaces","authors":"Marat Pliev ,&nbsp;Fedor Sukochev ,&nbsp;Anna Tomskova","doi":"10.1016/j.jfa.2025.111178","DOIUrl":"10.1016/j.jfa.2025.111178","url":null,"abstract":"<div><div>In this article we study the homotopical properties of linear groups of some Banach spaces. Our first main result asserts that for <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>&lt;</mo><mo>∞</mo></math></span> the linear group <span><math><mi>G</mi><mi>L</mi><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo><mo>)</mo></math></span> of the Lebesgue–Bochner space <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></math></span> is contractible to a point, where <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span> are both considered on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> equipped with the standard Lebesgue measure. The proof of this result is based on techniques drawn from the geometry of UMD-spaces. In addition, we establish the contractibility to a point of the general linear groups of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>&lt;</mo><mo>∞</mo></math></span>. The proof is based on the techniques drawn from the theory of vector-valued Köthe spaces. We also prove that for <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span> and for a reflexive symmetric sequence space <em>E</em> the linear group <span><math><mi>G</mi><mi>L</mi><mo>(</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo><mo>)</mo></math></span> is contractible to a point, where <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> is the space of <em>p</em>-summable sequences and <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>E</mi><mo>)</mo></math></span> is the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-sum of <em>E</em> spaces. As a consequence of the latter result we deduce the contractibility to a point of the linear group of a Besov space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>q</mi></mrow></msubsup></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>&lt;</mo><mo>∞</mo></math></span>, <span><math><mi>s</mi><mo>&gt;</mo><mn>0</mn></math></span>. We conclude with few open problems.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111178"},"PeriodicalIF":1.6,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924954","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":"Spectrum of invertible weighted composition operators on the unit disk","authors":"Jesús Oliva-Maza","doi":"10.1016/j.jfa.2025.111186","DOIUrl":"10.1016/j.jfa.2025.111186","url":null,"abstract":"<div><div>The spectrum of invertible weighted composition operators <span><math><mi>u</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> acting on classical Banach spaces of holomorphic functions in the unit disk <span><math><mi>D</mi></math></span> has been studied intensively over the years. Complete descriptions of that spectrum have been given in the elliptic or parabolic cases, that is, for <em>φ</em> either elliptic or parabolic, but only partial results have been obtained in the remaining case, that is, for hyperbolic <em>φ</em>. In this paper, we give the spectrum and the essential spectrum of <span><math><mi>u</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> for hyperbolic <em>φ</em>. Our results answer in the positive several conjectures posed by different authors.</div><div>In order to deal with the above questions, we present new techniques which involve the embedding of the weight <em>u</em> into a cocycle <span><math><msub><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>t</mi><mo>∈</mo><mi>R</mi></mrow></msub></math></span> associated to an hyperbolic flow <span><math><msub><mrow><mo>(</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>t</mi><mo>∈</mo><mi>R</mi></mrow></msub></math></span>. We also provide information about the range spaces and null spaces of <span><math><mi>λ</mi><mo>−</mo><mi>u</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> for <em>λ</em> lying in the interior of <span><math><mi>σ</mi><mo>(</mo><mi>u</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>φ</mi></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111186"},"PeriodicalIF":1.6,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020129","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":"Opening gaps in the spectrum of strictly ergodic Jacobi and CMV matrices","authors":"David Damanik ,&nbsp;Long Li","doi":"10.1016/j.jfa.2025.111182","DOIUrl":"10.1016/j.jfa.2025.111182","url":null,"abstract":"<div><div>We prove that dynamically defined Jacobi and CMV matrices associated with generic continuous sampling functions have all gaps predicted by the Gap Labeling Theorem open. We also give a mechanism for generic gap opening for quasi-periodic analytic sampling functions in the subcritical region following from the analyticity of resonance tongue boundaries for both Jacobi and CMV matrices.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111182"},"PeriodicalIF":1.6,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925224","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":"Partial boundary regularity for the Navier–Stokes equations in irregular domains","authors":"Dominic Breit","doi":"10.1016/j.jfa.2025.111188","DOIUrl":"10.1016/j.jfa.2025.111188","url":null,"abstract":"<div><div>We prove partial regularity of suitable weak solutions to the Navier–Stokes equations at the boundary in irregular domains. In particular, we provide a criterion which yields continuity of the velocity field in a boundary point and obtain solutions which are continuous in a.a. boundary point (their existence is a consequence of a new maximal regularity result for the Stokes equations in domains with minimal regularity). We suppose that we have a Lipschitz boundary which belongs to the fractional Sobolev space <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>p</mi><mo>,</mo><mi>p</mi></mrow></msup></math></span> for some <span><math><mi>p</mi><mo>&gt;</mo><mfrac><mrow><mn>15</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math></span>. The same result was previously only known under the much stronger assumption of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-boundary.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111188"},"PeriodicalIF":1.6,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924949","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":"Variational problem with repulsive-attractive kernels and its application","authors":"Daomin Cao ,&nbsp;Huifang Jia ,&nbsp;Xiao Luo","doi":"10.1016/j.jfa.2025.111187","DOIUrl":"10.1016/j.jfa.2025.111187","url":null,"abstract":"<div><div>In this paper, we continue our previous work <span><span>[6]</span></span>, <span><span>[25]</span></span>, <span><span>[35]</span></span>, and focus on standing waves with prescribed mass for the Hartree equation with Repulsive-attractive kernels, which are used in particle physics to describe the nonlocal interaction among particles <span><span>[22]</span></span>. First, we consider a family of interaction functionals consisting of power-law potentials with attractive and repulsive parts and establish the existence of global minimizers. By relaxing the uniform boundedness and radial symmetry conditions, we prove a conjecture raised by Choksi-Fetecau-Topaloglu in <span><span>[14]</span></span>. Then as an application, based on classification of attractive part in the kernel, a complete study on existence and qualitative analysis of standing waves for the Hartree equation with repulsive-attractive kernels are given. With respect to the case of single or purely attractive kernels considered in <span><span>[6]</span></span>, <span><span>[25]</span></span>, <span><span>[35]</span></span>, the competition between the two parts in repulsive-attractive kernels forces new implements to catch the solutions and analyze their Lane-Emden (or Hartree) profiles as particles gather (or dissipate).</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111187"},"PeriodicalIF":1.6,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924953","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":"Norm estimates for a broad class of modulation spaces, and continuity of Fourier type operators","authors":"Joachim Toft ,&nbsp;Christine Pfeuffer ,&nbsp;Nenad Teofanov","doi":"10.1016/j.jfa.2025.111177","DOIUrl":"10.1016/j.jfa.2025.111177","url":null,"abstract":"<div><div>We consider a broad class of modulation spaces <span><math><mi>M</mi><mo>(</mo><mi>ω</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span>, parameterized with weight function <em>ω</em> and a normal quasi-Banach function space <span><math><mi>B</mi></math></span> of order <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. Then we prove that <span><math><mi>f</mi><mo>∈</mo><mi>M</mi><mo>(</mo><mi>ω</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span>, if and only if <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mi>f</mi></math></span> belongs to the Wiener amalgam space <span><math><msup><mrow><mi>W</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>(</mo><mi>ω</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span>, and<span><span><span><math><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>M</mi><mo>(</mo><mi>ω</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></msub><mo>≍</mo><msub><mrow><mo>‖</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mi>f</mi><mspace></mspace><mo>⋅</mo><mspace></mspace><mi>ω</mi><mo>‖</mo></mrow><mrow><mi>B</mi></mrow></msub><mo>≍</mo><msub><mrow><mo>‖</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mi>f</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>W</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>(</mo><mi>ω</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></msub><mo>,</mo><mspace></mspace><mi>r</mi><mo>∈</mo><mo>[</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>∞</mo><mo>]</mo><mo>.</mo></math></span></span></span></div><div>We use the results to extend and improve continuity and lifting properties for pseudo-differential and Toeplitz operators with symbols in weighted <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>∞</mo><mo>,</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup></math></span>-spaces, <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>1</mn></math></span>, when acting on <span><math><mi>M</mi><mo>(</mo><mi>ω</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span>-spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111177"},"PeriodicalIF":1.6,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046956","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":"Derivation of the homogeneous kinetic wave equation: Longer time scales","authors":"Charles Collot ,&nbsp;Pierre Germain","doi":"10.1016/j.jfa.2025.111179","DOIUrl":"10.1016/j.jfa.2025.111179","url":null,"abstract":"<div><div>We consider the nonlinear Schrödinger equation set on a flat torus, in the regime which is conjectured to lead to the kinetic wave equation; in particular, the data are random, and spread up to high frequency in a weakly nonlinear regime. We pursue the investigations of our previous paper, and show that, in the case where the torus is the standard one, only the scaling considered there allows convergence of each diagram in the Dyson series up to the kinetic time scale. We also show that, for generic quadratic dispersion relations (non rectangular tori), the Dyson series converges on significantly longer time scales; we are able to reach the kinetic time up to an arbitrarily small polynomial error for a larger set of scalings. These results show the importance of the exact structure of the dispersion relation, more specifically of equidistribution properties of some bilinear quantities akin to pair correlations derived from it.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111179"},"PeriodicalIF":1.6,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046536","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}