Pub Date : 2026-03-15Epub Date: 2025-12-08DOI: 10.1016/j.jfa.2025.111300
Fernando de Ávila Silva , Marco Cappiello , Alexandre Kirilov
We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of singular solutions, we fully characterize when the system fails to be globally hypoelliptic.
{"title":"Global hypoellipticity for systems in time-periodic Gelfand-Shilov spaces","authors":"Fernando de Ávila Silva , Marco Cappiello , Alexandre Kirilov","doi":"10.1016/j.jfa.2025.111300","DOIUrl":"10.1016/j.jfa.2025.111300","url":null,"abstract":"<div><div>We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of singular solutions, we fully characterize when the system fails to be globally hypoelliptic.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111300"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145734878","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 : 2026-03-15Epub Date: 2025-12-08DOI: 10.1016/j.jfa.2025.111310
Jingbo Xia
We settle the issue of Berger-Coburn phenomenon on the Fock space completely for general symmetrically normed ideals , where Φ is not equivalent to . We show that if the Boyd indices of satisfy the condition , then for , we have if and only if . We further show that if either or , then there is an such that while .
{"title":"Boyd indices and the Berger-Coburn phenomenon","authors":"Jingbo Xia","doi":"10.1016/j.jfa.2025.111310","DOIUrl":"10.1016/j.jfa.2025.111310","url":null,"abstract":"<div><div>We settle the issue of Berger-Coburn phenomenon on the Fock space completely for general symmetrically normed ideals <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span>, where Φ is not equivalent to <span><math><msub><mrow><mi>Φ</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>. We show that if the Boyd indices of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span> satisfy the condition <span><math><mn>1</mn><mo><</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>Φ</mi></mrow></msub><mo><</mo><mo>∞</mo></math></span>, then for <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, we have <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span> if and only if <span><math><msub><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><mo>∈</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span>. We further show that if either <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> or <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>Φ</mi></mrow></msub><mo>=</mo><mo>∞</mo></math></span>, then there is an <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> such that <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span> while <span><math><msub><mrow><mi>H</mi></mrow><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><mo>∉</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>Φ</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111310"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145734877","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 : 2026-03-15Epub Date: 2025-11-19DOI: 10.1016/j.jfa.2025.111282
Giacomo Ascione , Atsuhide Ishida , József Lőrinczi
We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz potentials. These definitions rely on precise resolvent estimates, which we present in detail. We obtain these classes for diverse ranges of fractional exponent in dimensions , and for the physical operators with fractional exponent in dimensions one and two as limiting cases resulting under Γ-convergence. We show that Coulomb-type potentials are elements of fractional Rollnik-class up to but not including the critical singularity of the Hardy potential. In a second part of the paper we derive detailed results on the self-adjointness and spectral properties of relativistic Schrödinger operators obtained under perturbations by fractional Rollnik potentials. We also define an extended fractional Rollnik-class which is the maximal space for the Hilbert-Schmidt property of the related Birman-Schwinger operators.
{"title":"Special potentials for relativistic Laplacians I: Fractional Rollnik-class","authors":"Giacomo Ascione , Atsuhide Ishida , József Lőrinczi","doi":"10.1016/j.jfa.2025.111282","DOIUrl":"10.1016/j.jfa.2025.111282","url":null,"abstract":"<div><div>We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz potentials. These definitions rely on precise resolvent estimates, which we present in detail. We obtain these classes for diverse ranges of fractional exponent in dimensions <span><math><mn>1</mn><mo>≤</mo><mi>d</mi><mo>≤</mo><mn>3</mn></math></span>, and for the physical operators with fractional exponent <span><math><mi>α</mi><mo>=</mo><mn>1</mn></math></span> in dimensions one and two as limiting cases resulting under Γ-convergence. We show that Coulomb-type potentials are elements of fractional Rollnik-class up to but not including the critical singularity of the Hardy potential. In a second part of the paper we derive detailed results on the self-adjointness and spectral properties of relativistic Schrödinger operators obtained under perturbations by fractional Rollnik potentials. We also define an extended fractional Rollnik-class which is the maximal space for the Hilbert-Schmidt property of the related Birman-Schwinger operators.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111282"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683572","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 : 2026-03-15Epub Date: 2025-12-08DOI: 10.1016/j.jfa.2025.111302
Jerry R. Muir Jr.
We provide an assortment of integral representations of continuous linear functionals on complex and real subspaces of the space of holomorphic mappings from the open Euclidean unit ball of into . For complex or real linear functionals ℓ, our main results give representations of the form respectively, where μ is a complex Borel measure in the complex case or a finite signed or positive Borel measure in the real case, is a sphere centered at the origin, and the Hermitian inner product in is denoted in the integrands. The complex representation broadly applies to closed complex subspaces of , while the real versions assume various restrictions on real subspaces of whose necessity is explored. Several other representations stem from the main results.
{"title":"Integral representations of linear functionals on spaces of holomorphic mappings in the unit ball of Cn","authors":"Jerry R. Muir Jr.","doi":"10.1016/j.jfa.2025.111302","DOIUrl":"10.1016/j.jfa.2025.111302","url":null,"abstract":"<div><div>We provide an assortment of integral representations of continuous linear functionals on complex and real subspaces of the space <span><math><mi>H</mi><mo>(</mo><mi>B</mi><mo>,</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> of holomorphic mappings from the open Euclidean unit ball <span><math><mi>B</mi></math></span> of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> into <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. For complex or real linear functionals <em>ℓ</em>, our main results give representations of the form<span><span><span><math><mi>ℓ</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><munder><mo>∫</mo><mrow><mi>K</mi></mrow></munder><mo>〈</mo><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>,</mo><mi>z</mi><mo>〉</mo><mspace></mspace><mi>d</mi><mi>μ</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>ℓ</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><munder><mo>∫</mo><mrow><mi>K</mi></mrow></munder><mi>Re</mi><mo>〈</mo><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>,</mo><mi>z</mi><mo>〉</mo><mspace></mspace><mi>d</mi><mi>μ</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>,</mo></math></span></span></span> respectively, where <em>μ</em> is a complex Borel measure in the complex case or a finite signed or positive Borel measure in the real case, <span><math><mi>K</mi><mo>⊆</mo><mover><mrow><mi>B</mi></mrow><mo>‾</mo></mover></math></span> is a sphere centered at the origin, and the Hermitian inner product in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is denoted in the integrands. The complex representation broadly applies to closed complex subspaces of <span><math><mi>H</mi><mo>(</mo><mi>B</mi><mo>,</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, while the real versions assume various restrictions on real subspaces of <span><math><mi>H</mi><mo>(</mo><mi>B</mi><mo>,</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> whose necessity is explored. Several other representations stem from the main results.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111302"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145734875","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 : 2026-03-15Epub Date: 2025-11-19DOI: 10.1016/j.jfa.2025.111288
E. Başakoğlu , C. Sun , N. Tzvetkov , Y. Wang
We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain , . Using tools developed in the study of nonlinear dispersive PDEs, we establish local well-posedness in for and , thereby addressing, in particular, a question posed by Gualdani–Mischler–Mouhot [25]. To reach the result, the main tool we establish is the Strichartz estimate for solutions to the corresponding linear equation.
{"title":"Local well-posedness for the periodic Boltzmann equation with constant collision kernel","authors":"E. Başakoğlu , C. Sun , N. Tzvetkov , Y. Wang","doi":"10.1016/j.jfa.2025.111288","DOIUrl":"10.1016/j.jfa.2025.111288","url":null,"abstract":"<div><div>We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>. Using tools developed in the study of nonlinear dispersive PDEs, we establish local well-posedness in <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>v</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>r</mi></mrow></msubsup><msubsup><mrow><mi>H</mi></mrow><mrow><mi>x</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math></span> for <span><math><mi>s</mi><mo>></mo><mfrac><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math></span> and <span><math><mi>r</mi><mo>></mo><mfrac><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, thereby addressing, in particular, a question posed by Gualdani–Mischler–Mouhot <span><span>[25]</span></span>. To reach the result, the main tool we establish is the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> Strichartz estimate for solutions to the corresponding linear equation.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111288"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145651769","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 : 2026-03-15Epub Date: 2025-12-12DOI: 10.1016/j.jfa.2025.111311
Detlef Müller
As main result, we show that a pseudodifferential operator in the Weyl calculus, whose symbol has compact Fourier support, lies in the Schatten class if and only if its symbol lies in the Lebesgue space on phase space.
As an immediate consequence, this gives an alternative and very lucid proof of a recent result by Luef and Samuelsen who had discovered that for compactly supported measures μ, classical Fourier restriction estimates with respect to the measure μ are equivalent to quantum restriction estimates for the Fourier-Wigner transform for Schatten classes. Our approach also leads to substantially improved constants in the corresponding estimates which only grow polynomially in the diameter of the support of the measure μ.
{"title":"Bounds on pseudodifferential operators and Fourier restriction for Schatten classes","authors":"Detlef Müller","doi":"10.1016/j.jfa.2025.111311","DOIUrl":"10.1016/j.jfa.2025.111311","url":null,"abstract":"<div><div>As main result, we show that a pseudodifferential operator in the Weyl calculus, whose symbol has compact Fourier support, lies in the Schatten class <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> if and only if its symbol lies in the Lebesgue space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> on phase space.</div><div>As an immediate consequence, this gives an alternative and very lucid proof of a recent result by Luef and Samuelsen who had discovered that for compactly supported measures <em>μ</em>, classical Fourier restriction estimates with respect to the measure <em>μ</em> are equivalent to quantum restriction estimates for the Fourier-Wigner transform for Schatten classes. Our approach also leads to substantially improved constants in the corresponding estimates which only grow polynomially in the diameter of the support of the measure <em>μ</em>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111311"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837246","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 : 2026-03-15Epub Date: 2025-12-08DOI: 10.1016/j.jfa.2025.111304
Tarek M. Elgindi , Milton C. Lopes Filho , Helena J. Nussenzveig Lopes
A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of small viscosity. In this article we present a proof of absence of anomalous dissipation for 2D flows on the torus, with an arbitrary non-negative measure plus an integrable function as initial vorticity and square-integrable initial velocity. Our result applies to flows with forcing and provides an explicit estimate for the dissipation at small viscosity. The proof relies on a new refinement of a classical inequality due to J. Nash.
{"title":"Absence of anomalous dissipation for vortex sheets","authors":"Tarek M. Elgindi , Milton C. Lopes Filho , Helena J. Nussenzveig Lopes","doi":"10.1016/j.jfa.2025.111304","DOIUrl":"10.1016/j.jfa.2025.111304","url":null,"abstract":"<div><div>A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of small viscosity. In this article we present a proof of absence of anomalous dissipation for 2D flows on the torus, with an arbitrary non-negative measure plus an integrable function as initial vorticity and square-integrable initial velocity. Our result applies to flows with forcing and provides an explicit estimate for the dissipation at small viscosity. The proof relies on a new refinement of a classical inequality due to J. Nash.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111304"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837254","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 : 2026-03-15Epub Date: 2025-12-11DOI: 10.1016/j.jfa.2025.111312
Yangkendi Deng , Boning Di , Chenjie Fan , Zehua Zhao
We continue our study of bilinear estimates on the waveguide started in [12], [13]. The main point of the current article is, compared to previous work [12], that we obtain estimates beyond the semiclassical time regime. Our estimate is sharp in the sense that one can construct examples that saturate this estimate.
{"title":"Bilinear estimate for Schrödinger equation on R×T","authors":"Yangkendi Deng , Boning Di , Chenjie Fan , Zehua Zhao","doi":"10.1016/j.jfa.2025.111312","DOIUrl":"10.1016/j.jfa.2025.111312","url":null,"abstract":"<div><div>We continue our study of bilinear estimates on the waveguide <span><math><mi>R</mi><mo>×</mo><mi>T</mi></math></span> started in <span><span>[12]</span></span>, <span><span>[13]</span></span>. The main point of the current article is, compared to previous work <span><span>[12]</span></span>, that we obtain estimates beyond the semiclassical time regime. Our estimate is sharp in the sense that one can construct examples that saturate this estimate.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111312"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145787933","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 : 2026-03-15Epub Date: 2025-12-10DOI: 10.1016/j.jfa.2025.111301
Yacin Ameur, Joakim Cronvall
We consider a class of external potentials on the complex plane for which the coincidence set to the obstacle problem contains a Jordan curve in the exterior of the droplet. We refer to this curve as a spectral outpost. We study the corresponding Coulomb gas at .
Generalizing recent work in the radially symmetric case, we prove that the number of particles which fall near the spectral outpost has an asymptotic Heine distribution, as the number of particles .
We also consider a class of potentials with disconnected droplets whose connected components are separated by a ring-shaped spectral gap. We prove that the fluctuations of the number of particles that fall near a given component has an asymptotic discrete normal distribution, which depends on n.
For the case of disconnected droplets we also consider fluctuations of general smooth linear statistics and show that they tend to distribute as the sum of a Gaussian field and an independent, oscillatory, discrete Gaussian field.
Our methods involve a new asymptotic formula on the norm of monic orthogonal polynomials in the bifurcation regime and a variant of the method of limit Ward identities of Ameur, Hedenmalm, and Makarov.
{"title":"On fluctuations of Coulomb systems and universality of the Heine distribution","authors":"Yacin Ameur, Joakim Cronvall","doi":"10.1016/j.jfa.2025.111301","DOIUrl":"10.1016/j.jfa.2025.111301","url":null,"abstract":"<div><div>We consider a class of external potentials on the complex plane <span><math><mi>C</mi></math></span> for which the coincidence set to the obstacle problem contains a Jordan curve in the exterior of the droplet. We refer to this curve as a spectral outpost. We study the corresponding Coulomb gas at <span><math><mi>β</mi><mo>=</mo><mn>2</mn></math></span>.</div><div>Generalizing recent work in the radially symmetric case, we prove that the number of particles which fall near the spectral outpost has an asymptotic Heine distribution, as the number of particles <span><math><mi>n</mi><mo>→</mo><mo>∞</mo></math></span>.</div><div>We also consider a class of potentials with disconnected droplets whose connected components are separated by a ring-shaped spectral gap. We prove that the fluctuations of the number of particles that fall near a given component has an asymptotic discrete normal distribution, which depends on <em>n</em>.</div><div>For the case of disconnected droplets we also consider fluctuations of general smooth linear statistics and show that they tend to distribute as the sum of a Gaussian field and an independent, oscillatory, discrete Gaussian field.</div><div>Our methods involve a new asymptotic formula on the norm of monic orthogonal polynomials in the bifurcation regime and a variant of the method of limit Ward identities of Ameur, Hedenmalm, and Makarov.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111301"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145734873","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 : 2026-03-15Epub Date: 2025-12-09DOI: 10.1016/j.jfa.2025.111305
Li Wen , Yuan Wu
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on with certain slowly decaying long-range hopping and analytic cosine type potentials. As applications, we prove the arithmetic spectral localization, and obtain upper bounds on quantum dynamics for all phase parameters. To deal with quantum dynamics estimates, we develop an approach employing separation property (rather than the sublinear bound) of resonant blocks in the regime of Green's function estimates.
{"title":"Green's function estimates for long-range quasi-periodic operators on Zd and applications","authors":"Li Wen , Yuan Wu","doi":"10.1016/j.jfa.2025.111305","DOIUrl":"10.1016/j.jfa.2025.111305","url":null,"abstract":"<div><div>We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with certain slowly decaying long-range hopping and analytic cosine type potentials. As applications, we prove the arithmetic spectral localization, and obtain upper bounds on quantum dynamics for all phase parameters. To deal with quantum dynamics estimates, we develop an approach employing separation property (rather than the sublinear bound) of resonant blocks in the regime of Green's function estimates.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 6","pages":"Article 111305"},"PeriodicalIF":1.6,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145734874","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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