Journal of Functional Analysis最新文献

{"title":"A degree counting formula for Fuchsian ODEs with unitarizable monodromy","authors":"Hsin-Yuan Huang ,&nbsp;Chang-Shou Lin","doi":"10.1016/j.jfa.2025.110969","DOIUrl":"10.1016/j.jfa.2025.110969","url":null,"abstract":"<div><div>In this paper, we study the problem of whether the monodromy matrices of second-order Fuchsian ordinary differential equations (ODEs) are unitary. Let <em>k</em> be the number of non-integer differences of the local exponents at the singular points of the ODEs. By employing the Leray-Schauder degree formulas for the corresponding curvature equations, we show that under certain assumptions, the degree does not vanish when <span><math><mi>k</mi><mo>=</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></math></span>, which implies that the corresponding monodromy matrices are unitary. Among others, we show the form of the degree counting formulas. To the best of our knowledge, this is the first work that assigns the Leray-Schauder degree to Fuchsian ODEs from the perspective of the corresponding curvature equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110969"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143786173","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":"HCIZ integral formula as unitarity of a canonical map between reproducing kernel spaces","authors":"Martin Miglioli","doi":"10.1016/j.jfa.2025.110977","DOIUrl":"10.1016/j.jfa.2025.110977","url":null,"abstract":"<div><div>In this article we prove that the Harish-Chandra-Itzykson-Zuber (HCIZ) integral formula is equivalent to the unitarity of a canonical map between fixed point spaces of unitary representations on Segal-Bargmann spaces. As a consequence, we provide two new proofs of the HCIZ integral formula and alternative proofs of related results.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110977"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143786171","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":"Cauchy transforms and Szegő projections in dual Hardy spaces: Inequalities and Möbius invariance","authors":"David E. Barrett ,&nbsp;Luke D. Edholm","doi":"10.1016/j.jfa.2025.110980","DOIUrl":"10.1016/j.jfa.2025.110980","url":null,"abstract":"<div><div>Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a Möbius invariant function bounding the norm of the Cauchy transform <strong><em>C</em></strong> from below. This function is shown to satisfy strong rigidity properties and is closely connected via the Berezin transform to the square of the Kerzman-Stein operator. Explicit example calculations are presented. For ellipses, a new asymptotically sharp lower bound on the norm of <strong><em>C</em></strong> is produced.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110980"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sampling discretization in Orlicz spaces","authors":"Egor Kosov ,&nbsp;Sergey Tikhonov","doi":"10.1016/j.jfa.2025.110971","DOIUrl":"10.1016/j.jfa.2025.110971","url":null,"abstract":"<div><div>We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms. In particular, we are interested in the recovery by linear and nonlinear methods in the norms close to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110971"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815319","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":"Viscosity solution to complex Hessian equations on compact Hermitian manifolds","authors":"Jingrui Cheng,&nbsp;Yulun Xu","doi":"10.1016/j.jfa.2025.110936","DOIUrl":"10.1016/j.jfa.2025.110936","url":null,"abstract":"<div><div>We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution is shown to be unique when the right hand is strictly monotone increasing in terms of the solution. When the right hand side does not depend on the solution, we reduces it to the strict monotonicity of the solvability constant.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110936"},"PeriodicalIF":1.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738471","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":"Two new constant rank theorems","authors":"Qinfeng Li,&nbsp;Lu Xu","doi":"10.1016/j.jfa.2025.110935","DOIUrl":"10.1016/j.jfa.2025.110935","url":null,"abstract":"<div><div>Motivated from one-dimensional rigidity results of entire solutions to Liouville equation, we consider the semilinear equation<span><span><span>(0.1)</span><span><math><mrow><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>G</mi><mo>(</mo><mi>u</mi><mo>)</mo><mspace></mspace><mrow><mtext>in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mi>G</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>&lt;</mo><mn>0</mn></math></span> and <span><math><mi>G</mi><msup><mrow><mi>G</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>≤</mo><mi>A</mi><msup><mrow><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>, with <span><math><mi>A</mi><mo>&gt;</mo><mn>0</mn></math></span>. Let <em>u</em> be a smooth convex solution to <span><span>(0.1)</span></span> and <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> be the <em>k</em>-th elementary symmetric polynomial with respect to <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></math></span>. Under the above conditions, we prove the following two new constant rank theorems:<ul><li><span>(1)</span><span><div>If <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> has a local minimum, then <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></math></span> has constant rank 1 for <span><math><mi>A</mi><mo>≤</mo><mn>2</mn></math></span>.</div></span></li><li><span>(2)</span><span><div>If <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> has a local minimum, then <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> is always zero and <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></math></span> must have constant rank <span><math><mi>r</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span> in the domain for <span><math><mi>A</mi><mo>≤</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></mfrac></math></span>.</div></span></li></ul></div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110935"},"PeriodicalIF":1.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737989","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":"Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus","authors":"J. Huang ,&nbsp;Y. Nessipbayev ,&nbsp;F. Sukochev ,&nbsp;D. Zanin","doi":"10.1016/j.jfa.2025.110946","DOIUrl":"10.1016/j.jfa.2025.110946","url":null,"abstract":"<div><div>We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting; while the second resembles the Kolmogorov–Riesz compactness theorem (see <span><span>Theorem 4.1</span></span>, <span><span>Theorem 5.7</span></span>, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110946"},"PeriodicalIF":1.7,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Commutator estimates for Haar shifts with general measures","authors":"Tainara Borges ,&nbsp;José M. Conde Alonso ,&nbsp;Jill Pipher ,&nbsp;Nathan A. Wagner","doi":"10.1016/j.jfa.2025.110945","DOIUrl":"10.1016/j.jfa.2025.110945","url":null,"abstract":"<div><div>We study <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> estimates for the commutator <span><math><mo>[</mo><mi>H</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span>, where the operator <span><math><mi>H</mi></math></span> is a dyadic model of the classical Hilbert transform introduced in <span><span>[9]</span></span>, <span><span>[10]</span></span> and is adapted to a non-doubling Borel measure <em>μ</em> satisfying a dyadic regularity condition which is necessary for <span><math><mi>H</mi></math></span> to be bounded on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>. We show that <span><math><msub><mrow><mo>‖</mo><mo>[</mo><mi>H</mi><mo>,</mo><mi>b</mi><mo>]</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></msub><mo>≲</mo><msub><mrow><mo>‖</mo><mi>b</mi><mo>‖</mo></mrow><mrow><mrow><mi>BMO</mi></mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></msub></math></span>, but to <em>characterize</em> martingale BMO requires additional commutator information. We prove weighted inequalities for <span><math><mo>[</mo><mi>H</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span> together with a version of the John-Nirenberg inequality adapted to appropriate weight classes <span><math><msub><mrow><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>p</mi></mrow></msub></math></span> that we define for our non-homogeneous setting. This requires establishing reverse Hölder inequalities for these new weight classes. Finally, we revisit the appropriate class of nonhomogeneous measures <em>μ</em> for the study of different types of Haar shift operators.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110945"},"PeriodicalIF":1.7,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705772","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":"Quenched large deviation principles for random projections of ℓpn balls","authors":"Patrick Lopatto,&nbsp;Kavita Ramanan,&nbsp;Xiaoyu Xie","doi":"10.1016/j.jfa.2025.110937","DOIUrl":"10.1016/j.jfa.2025.110937","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be a sequence of positive integers growing to infinity at a sublinear rate, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Given a sequence of &lt;em&gt;n&lt;/em&gt;-dimensional random vectors &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; belonging to a certain class, which includes uniform distributions on suitably scaled &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-balls or &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-spheres, &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, and product distributions with sub-Gaussian marginals, we study the large deviations behavior of the corresponding sequence of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-dimensional orthogonal projections &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is an &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-dimensional projection matrix lying in the Stiefel manifold of orthonormal &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-frames in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. For almost every sequence of projection matrices, we establish a large deviation principle (LDP) for the corresponding sequence of projections, with a fairly explicit rate function that does not depend on the sequence of projection matrices. As corollaries, we also obtain quenched LDPs for sequences of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-norms and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-norms of the coordinates of the projections. Past work on LDPs for projections with growing dimension has mainly focused on ","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110937"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799252","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":"Quantum trajectories. Spectral gap, quasi-compactness & limit theorems","authors":"Tristan Benoist,&nbsp;Arnaud Hautecœur,&nbsp;Clément Pellegrini","doi":"10.1016/j.jfa.2025.110932","DOIUrl":"10.1016/j.jfa.2025.110932","url":null,"abstract":"<div><div>Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit a unique invariant measure under a purification and irreducibility assumptions. This paper is devoted to the spectral study of the underlying Markov operator. Using Quasi-compactness, it is shown that this operator admits a spectral gap and the peripheral spectrum is described in a precise manner. Next two perturbations of this operator are studied. This allows to derive limit theorems (Central Limit Theorem, Berry-Esseen bounds and Large Deviation Principle) for the empirical mean of functions of the Markov chain as well as the Lyapounov exponent of the underlying random dynamical system.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110932"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738468","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}