Pub Date : 2026-01-13DOI: 10.1016/j.jfa.2026.111357
Toan T. Nguyen
In this paper, we establish the large time asymptotic behavior of solutions to the linearized Vlasov-Poisson system near general spatially homogeneous equilibria with connected support on the torus or on the whole space , including those that are non-monotone. The problem can be solved completely mode by mode for each spatial wave number, and their longtime dynamics is intimately tied to the “survival threshold” of wave numbers computed by where ϒ is the maximal speed of particle velocities. It is shown that purely oscillatory electric fields exist and obey a Klein-Gordon's type dispersion relation for wave numbers below and up to the threshold, thus rigorously confirming the existence of Langmuir's oscillatory waves for a non-trivial range of spatial frequencies in this linearized setting. At the threshold, the phase velocity of these oscillatory waves enters the range of admissible particle velocities, namely there are particles that move at the same propagation speed of the waves. It is this exact resonant interaction between particles and the oscillatory fields that causes the waves to be damped, classically known as Landau damping. Landau's law of decay is explicitly computed and is sensitive to the decaying rate of the background equilibria. The faster it decays at the maximal velocity, the weaker Landau damping is. Beyond the threshold, the electric fields are a perturbation of those generated by the free transport dynamics and thus decay rapidly fast due to the phase mixing mechanism.
{"title":"Landau damping and survival threshold","authors":"Toan T. Nguyen","doi":"10.1016/j.jfa.2026.111357","DOIUrl":"10.1016/j.jfa.2026.111357","url":null,"abstract":"<div><div>In this paper, we establish the large time asymptotic behavior of solutions to the linearized Vlasov-Poisson system near general spatially homogeneous equilibria <span><math><mi>μ</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>|</mo><mi>v</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> with connected support on the torus <span><math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> or on the whole space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math></span>, including those that are non-monotone. The problem can be solved completely mode by mode for each spatial wave number, and their longtime dynamics is intimately tied to the “survival threshold” of wave numbers computed by<span><span><span><math><msubsup><mrow><mi>κ</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>4</mn><mi>π</mi><munderover><mo>∫</mo><mrow><mn>0</mn></mrow><mrow><mi>ϒ</mi></mrow></munderover><mfrac><mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>μ</mi><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><msup><mrow><mi>ϒ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mspace></mspace><mi>d</mi><mi>u</mi></math></span></span></span> where ϒ is the maximal speed of particle velocities. It is shown that purely oscillatory electric fields exist and obey a Klein-Gordon's type dispersion relation for wave numbers below and up to the threshold, thus rigorously confirming the existence of Langmuir's oscillatory waves for a non-trivial range of spatial frequencies in this linearized setting. At the threshold, the phase velocity of these oscillatory waves enters the range of admissible particle velocities, namely there are particles that move at the same propagation speed of the waves. It is this exact resonant interaction between particles and the oscillatory fields that causes the waves to be damped, classically known as Landau damping. Landau's law of decay is explicitly computed and is sensitive to the decaying rate of the background equilibria. The faster it decays at the maximal velocity, the weaker Landau damping is. Beyond the threshold, the electric fields are a perturbation of those generated by the free transport dynamics and thus decay rapidly fast due to the phase mixing mechanism.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111357"},"PeriodicalIF":1.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036481","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 : 2026-01-13DOI: 10.1016/j.jfa.2026.111351
Adimurthi, Prosenjit Roy, Vivek Sahu
We establish generalized fractional boundary Hardy-type inequality, in the spirit of Caffarelli-Kohn-Nirenberg inequality for different values of s and p on various domains in . In particular, for Lipschitz bounded domains any values of s and p are admissible, settling all the cases in subcritical, supercritical and critical regime. In this paper we have solved the open problems posed by Dyda for the critical case . Moreover we have proved the embeddings of in subcritical, critical and supercritical uniformly without using Dyda's decomposition. Additionally, we extend our results to include a weighted fractional boundary Hardy-type inequality for the critical case.
{"title":"Fractional boundary Hardy inequality for the critical cases","authors":"Adimurthi, Prosenjit Roy, Vivek Sahu","doi":"10.1016/j.jfa.2026.111351","DOIUrl":"10.1016/j.jfa.2026.111351","url":null,"abstract":"<div><div>We establish generalized fractional boundary Hardy-type inequality, in the spirit of Caffarelli-Kohn-Nirenberg inequality for different values of <em>s</em> and <em>p</em> on various domains in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>d</mi><mo>≥</mo><mn>1</mn></math></span>. In particular, for Lipschitz bounded domains any values of <em>s</em> and <em>p</em> are admissible, settling all the cases in subcritical, supercritical and critical regime. In this paper we have solved the open problems posed by Dyda for the critical case <span><math><mi>s</mi><mi>p</mi><mo>=</mo><mn>1</mn></math></span>. Moreover we have proved the embeddings of <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> in subcritical, critical and supercritical uniformly without using Dyda's decomposition. Additionally, we extend our results to include a weighted fractional boundary Hardy-type inequality for the critical case.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111351"},"PeriodicalIF":1.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036482","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 : 2026-01-13DOI: 10.1016/j.jfa.2026.111350
Eleonora Ficola, Thomas Schmidt
We study the minimization of anisotropic total variation functionals with additional measure terms among functions of bounded variation subject to a Dirichlet boundary condition. More specifically, we identify and characterize certain isoperimetric conditions, which prove to be sharp assumptions on the signed measure data in connection with semicontinuity, existence, and relaxation results. Furthermore, we present a variety of examples which elucidate our assumptions and results.
{"title":"Lower semicontinuity and existence results for anisotropic TV functionals with signed measure data","authors":"Eleonora Ficola, Thomas Schmidt","doi":"10.1016/j.jfa.2026.111350","DOIUrl":"10.1016/j.jfa.2026.111350","url":null,"abstract":"<div><div>We study the minimization of anisotropic total variation functionals with additional measure terms among functions of bounded variation subject to a Dirichlet boundary condition. More specifically, we identify and characterize certain isoperimetric conditions, which prove to be sharp assumptions on the signed measure data in connection with semicontinuity, existence, and relaxation results. Furthermore, we present a variety of examples which elucidate our assumptions and results.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111350"},"PeriodicalIF":1.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036489","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 : 2026-01-13DOI: 10.1016/j.jfa.2026.111353
Ning Li , Chuijia Wang
The notion of transfer is a way to relate representations of different real forms of a complex semisimple Lie group. It has been investigated that there is a close connection between local theta correspondence and the procedure of transfer by the pioneer work of Wallach–Zhu. In this paper, we focus on the transfer of irreducible unitary constituents of the degenerate principal series representations of . In particular, we show that every irreducible unitary constituent of the big theta lift from to of the trivial character can be realized as a transfer of the small theta lift from the compact orthogonal group to of the trivial character via the study of K-types. This partially confirms a conjecture of Wallach–Zhu on the internal structure of theta lifts in the non-stable range case.
{"title":"Transfer between theta lifts of trivial representations","authors":"Ning Li , Chuijia Wang","doi":"10.1016/j.jfa.2026.111353","DOIUrl":"10.1016/j.jfa.2026.111353","url":null,"abstract":"<div><div>The notion of transfer is a way to relate representations of different real forms of a complex semisimple Lie group. It has been investigated that there is a close connection between local theta correspondence and the procedure of transfer by the pioneer work of Wallach–Zhu. In this paper, we focus on the transfer of irreducible unitary constituents of the degenerate principal series representations of <span><math><mrow><mi>Sp</mi></mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>,</mo><mi>R</mi><mo>)</mo></math></span>. In particular, we show that every irreducible unitary constituent of the big theta lift from <span><math><mi>O</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> to <span><math><mrow><mi>Sp</mi></mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>,</mo><mi>R</mi><mo>)</mo></math></span> of the trivial character can be realized as a transfer of the small theta lift from the compact orthogonal group <span><math><mi>O</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>p</mi><mo>+</mo><mi>q</mi><mo>)</mo></math></span> to <span><math><mrow><mi>Sp</mi></mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>,</mo><mi>R</mi><mo>)</mo></math></span> of the trivial character via the study of <em>K</em>-types. This partially confirms a conjecture of Wallach–Zhu on the internal structure of theta lifts in the non-stable range case.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111353"},"PeriodicalIF":1.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036479","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 : 2026-01-12DOI: 10.1016/j.jfa.2026.111344
Jan Lang , Zdeněk Mihula
We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. spaces).
More specifically, we focus on studying the “quality” of non-compactness for optimal Sobolev embeddings , where X is a given r.i. space and is the corresponding optimal target r.i. space (i.e., the smallest among all r.i. spaces).
For the class of sub-limiting norms (i.e., the norms whose fundamental function satisfies as ), we construct suitable spike-function sequences that establish a general framework for proving non-strict singularity of optimal (and thus non-compact) sublimiting Sobolev embeddings.
As an application, we show that optimal sublimiting Sobolev embeddings are not strictly singular in a rather large subclass of r.i. spaces, namely weighted Lambda spaces , . Except for the endpoint case , our spike-function construction enables us to construct a subspace of that is isomorphic to , which we then leverage to prove the non-strict singularity of the corresponding optimal Sobolev embedding.
{"title":"Non-strict singularity of optimal Sobolev embeddings","authors":"Jan Lang , Zdeněk Mihula","doi":"10.1016/j.jfa.2026.111344","DOIUrl":"10.1016/j.jfa.2026.111344","url":null,"abstract":"<div><div>We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. spaces).</div><div>More specifically, we focus on studying the “quality” of non-compactness for optimal Sobolev embeddings <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mi>X</mi><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>→</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>, where <em>X</em> is a given r.i. space and <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is the corresponding optimal target r.i. space (i.e., the smallest among all r.i. spaces).</div><div>For the class of sub-limiting norms (i.e., the norms whose fundamental function satisfies <span><math><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>X</mi></mrow></msub></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>≈</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mi>m</mi><mo>/</mo><mi>n</mi></mrow></msup><msub><mrow><mi>φ</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> as <span><math><mi>t</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span>), we construct suitable spike-function sequences that establish a general framework for proving non-strict singularity of optimal (and thus non-compact) sublimiting Sobolev embeddings.</div><div>As an application, we show that optimal sublimiting Sobolev embeddings are not strictly singular in a rather large subclass of r.i. spaces, namely weighted Lambda spaces <span><math><mi>X</mi><mo>=</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>w</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span>, <span><math><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. Except for the endpoint case <span><math><mi>X</mi><mo>=</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>/</mo><mi>m</mi><mo>,</mo><mn>1</mn></mrow></msup></math></span>, our spike-function construction enables us to construct a subspace of <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mi>X</mi></math></span> that is isomorphic to <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>, which we then leverage to prove the non-strict singularity of the corresponding optimal Sobolev embedding.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111344"},"PeriodicalIF":1.6,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036485","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 : 2026-01-12DOI: 10.1016/j.jfa.2026.111354
Xiaoman Chen , Zelin Yi
By following a groupoid approach to pseudodifferential calculus developed by Van Erp and Yuncken, we study the parallel theory on the rescaled bundle and show that the rescaled bundle gives a geometric characterization of the asymptotic pseudodifferential calculus on spinor bundles by Block and Fox.
{"title":"Asymptotic pseudodifferential calculus and the rescaled bundle","authors":"Xiaoman Chen , Zelin Yi","doi":"10.1016/j.jfa.2026.111354","DOIUrl":"10.1016/j.jfa.2026.111354","url":null,"abstract":"<div><div>By following a groupoid approach to pseudodifferential calculus developed by Van Erp and Yuncken, we study the parallel theory on the rescaled bundle and show that the rescaled bundle gives a geometric characterization of the asymptotic pseudodifferential calculus on spinor bundles by Block and Fox.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111354"},"PeriodicalIF":1.6,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036484","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 : 2026-01-01Epub Date: 2025-09-17DOI: 10.1016/j.jfa.2025.111199
Chuanhuan Li , Yi Li
In this paper, we derive a pinching estimate for the traceless Ricci curvature in terms of scalar curvature and the norm of the Weyl tensor under the Laplacian flow for closed structures. Then we apply this estimate to study the long time existence of the Laplacian flow and prove that the norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.
{"title":"Curvature pinching estimate under the Laplacian G2 flow","authors":"Chuanhuan Li , Yi Li","doi":"10.1016/j.jfa.2025.111199","DOIUrl":"10.1016/j.jfa.2025.111199","url":null,"abstract":"<div><div>In this paper, we derive a pinching estimate for the traceless Ricci curvature in terms of scalar curvature and the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor under the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow for closed <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> structures. Then we apply this estimate to study the long time existence of the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow and prove that the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111199"},"PeriodicalIF":1.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155318","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 : 2026-01-01Epub Date: 2025-09-01DOI: 10.1016/j.jfa.2025.111180
Giorgio Cipolloni , László Erdős , Yuanyuan Xu
We consider the standard overlap of any bi-orthogonal family of left and right eigenvectors of a large random matrix X 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 [15], as well as Benaych-Georges and Zeitouni [13], 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 X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge.
{"title":"Optimal decay of eigenvector overlap for non-Hermitian random matrices","authors":"Giorgio Cipolloni , László Erdős , 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":"2026-01-01","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}
Pub Date : 2026-01-01Epub Date: 2025-09-03DOI: 10.1016/j.jfa.2025.111184
Teun D.H. van Nuland, Lorenzo Pettinari
In [3] it is claimed incorrectly that the Berezin quantization map maps surjectively to the resolvent algebra.1 We show here that it does not. Similarly, the Berezin map defined on does not reach all compact operators, contrary to what is claimed in [2, II.(2.73)].2 We moreover fill a gap in the proof of injectivity of the Berezin quantization map on of [3].
{"title":"Corrigendum to: “Quantization and the resolvent algebra” [J. Funct. Anal. 277 (8) (2019) 2815–2838]","authors":"Teun D.H. van Nuland, 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><sup>1</sup></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><sup>2</sup></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":"2026-01-01","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}
Pub Date : 2026-01-01Epub Date: 2025-08-29DOI: 10.1016/j.jfa.2025.111186
Jesús Oliva-Maza
The spectrum of invertible weighted composition operators acting on classical Banach spaces of holomorphic functions in the unit disk has been studied intensively over the years. Complete descriptions of that spectrum have been given in the elliptic or parabolic cases, that is, for φ either elliptic or parabolic, but only partial results have been obtained in the remaining case, that is, for hyperbolic φ. In this paper, we give the spectrum and the essential spectrum of for hyperbolic φ. Our results answer in the positive several conjectures posed by different authors.
In order to deal with the above questions, we present new techniques which involve the embedding of the weight u into a cocycle associated to an hyperbolic flow . We also provide information about the range spaces and null spaces of for λ lying in the interior of .
{"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":"2026-01-01","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}