Pub Date : 2026-04-15Epub Date: 2026-01-13DOI: 10.1016/j.jfa.2026.111355
Magnus Goffeng , Bram Mesland , Mehmet Haluk Şengün
In analogy with the factorization of representations of adelic groups as restricted products of representations of local groups, we study restricted tensor products of Hilbert -modules and of -correspondences. The construction produces global -correspondences from compatible collections of local -correspondences. When applied to the collection of -correspondences capturing local parabolic induction, the construction produces a global -correspondence that captures adelic parabolic induction.
与将非对称群的表示分解为局部群的表示的限制积类似，我们研究了Hilbert C -模和C -对应的限制张量积。施工生产全球C⁎通讯从兼容的集合当地C⁎通讯。当应用于捕获局部抛物线感应的C -对应集合时，该构造产生捕获非抛物线感应的全局C -对应。
{"title":"Adelic C⁎-correspondences and parabolic induction","authors":"Magnus Goffeng , Bram Mesland , Mehmet Haluk Şengün","doi":"10.1016/j.jfa.2026.111355","DOIUrl":"10.1016/j.jfa.2026.111355","url":null,"abstract":"<div><div>In analogy with the factorization of representations of adelic groups as restricted products of representations of local groups, we study restricted tensor products of Hilbert <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-modules and of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-correspondences. The construction produces global <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-correspondences from compatible collections of local <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-correspondences. When applied to the collection of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-correspondences capturing local parabolic induction, the construction produces a global <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-correspondence that captures adelic parabolic induction.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111355"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969418","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 : 2026-04-15Epub Date: 2026-01-13DOI: 10.1016/j.jfa.2026.111347
Xinjie Jiang , Changzheng Qu , Yun Yang
In this paper, the existence and uniqueness for a specific centro-affine invariant hypersurface flow in are studied, and the corresponding evolutionary processes in both centro-affine and Euclidean settings are explored. It turns out that this flow exhibits similar properties to the standard heat flow. In addition, the long time existence of this flow is investigated, which shows that the hypersurface governed by this flow becomes asymptotically ellipsoidal via systematically investigating evolutions of centro-affine invariants. Furthermore, a classification of eternal solutions for this flow is provided.
{"title":"An eternal hypersurface flow arising in centro-affine geometry","authors":"Xinjie Jiang , Changzheng Qu , Yun Yang","doi":"10.1016/j.jfa.2026.111347","DOIUrl":"10.1016/j.jfa.2026.111347","url":null,"abstract":"<div><div>In this paper, the existence and uniqueness for a specific centro-affine invariant hypersurface flow in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> are studied, and the corresponding evolutionary processes in both centro-affine and Euclidean settings are explored. It turns out that this flow exhibits similar properties to the standard heat flow. In addition, the long time existence of this flow is investigated, which shows that the hypersurface governed by this flow becomes asymptotically ellipsoidal via systematically investigating evolutions of centro-affine invariants. Furthermore, a classification of eternal solutions for this flow is provided.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111347"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969416","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 : 2026-04-15Epub Date: 2026-01-23DOI: 10.1016/j.jfa.2026.111381
Han Hong , Gaoming Wang
We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension has for some and mean convex boundary, then it is either isometric to for a closed manifold Σ with nonnegative Ricci curvature or it has no interior ends.
{"title":"A splitting theorem for manifolds with nonnegative spectral Ricci curvature and mean convex boundary","authors":"Han Hong , Gaoming Wang","doi":"10.1016/j.jfa.2026.111381","DOIUrl":"10.1016/j.jfa.2026.111381","url":null,"abstract":"<div><div>We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> has <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mo>−</mo><mi>α</mi><mi>Δ</mi><mo>+</mo><mi>Ric</mi><mo>)</mo><mo>≥</mo><mn>0</mn></math></span> for some <span><math><mi>α</mi><mo><</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></mfrac></math></span> and mean convex boundary, then it is either isometric to <span><math><mi>Σ</mi><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>≥</mo><mn>0</mn></mrow></msub></math></span> for a closed manifold Σ with nonnegative Ricci curvature or it has no interior ends.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111381"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075049","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 : 2026-04-15Epub Date: 2026-01-21DOI: 10.1016/j.jfa.2026.111362
Benedetta Noris , Giovanni Siclari , Gianmaria Verzini
We consider the well-known shape optimization problem with spectral cost: minimizing the first eigenvalue of the Dirichlet Laplacian among all subdomains Ω having prescribed volume and contained in a fixed box D; equivalently, we look for the best way to remove a compact set (obstacle) of Lebesgue measure , , in order to minimize the first Dirichlet eigenvalue of the set .
In the small volume regime , we prove that the optimal obstacles accumulate, in a suitable sense, to points of ∂D where is minimal, where denotes the first eigenfunction of the Dirichlet Laplacian on D. Moreover, we provide a fairly detailed description of the convergence of the optimal eigenvalues, eigenfunctions and free boundaries. Our results are based on sharp estimates of the optimal eigenvalues, in terms of a suitable notion of relative capacity.
{"title":"Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle","authors":"Benedetta Noris , Giovanni Siclari , Gianmaria Verzini","doi":"10.1016/j.jfa.2026.111362","DOIUrl":"10.1016/j.jfa.2026.111362","url":null,"abstract":"<div><div>We consider the well-known shape optimization problem with spectral cost: minimizing the first eigenvalue of the Dirichlet Laplacian among all subdomains Ω having prescribed volume and contained in a fixed box <em>D</em>; equivalently, we look for the best way to remove a compact set (obstacle) <span><math><mi>K</mi><mo>⊂</mo><mover><mrow><mi>D</mi></mrow><mo>‾</mo></mover></math></span> of Lebesgue measure <span><math><mo>|</mo><mi>K</mi><mo>|</mo><mo>=</mo><mi>ε</mi></math></span>, <span><math><mn>0</mn><mo><</mo><mi>ε</mi><mo><</mo><mo>|</mo><mi>D</mi><mo>|</mo></math></span>, in order to minimize the first Dirichlet eigenvalue of the set <span><math><mi>Ω</mi><mo>=</mo><mi>D</mi><mo>∖</mo><mi>K</mi></math></span>.</div><div>In the small volume regime <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, we prove that the optimal obstacles accumulate, in a suitable sense, to points of ∂<em>D</em> where <span><math><mo>|</mo><mi>∇</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>|</mo></math></span> is minimal, where <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> denotes the first eigenfunction of the Dirichlet Laplacian on <em>D</em>. Moreover, we provide a fairly detailed description of the convergence of the optimal eigenvalues, eigenfunctions and free boundaries. Our results are based on sharp estimates of the optimal eigenvalues, in terms of a suitable notion of relative capacity.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111362"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075050","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 : 2026-04-15Epub Date: 2026-01-14DOI: 10.1016/j.jfa.2026.111345
Ethan Sussman
Recent work by Hintz–Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schrödinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic analysis by providing full asymptotic expansions in every possible asymptotic regime. Moreover, the analysis is done in any dimension , for any asymptotically conic manifold, and we keep track of partial multipole expansions. Applications include full asymptotic analyses of the Schrödinger, wave, and Klein–Gordon equations, one of these being described in a companion paper. Using previous work, only partial asymptotic analyses were possible.
{"title":"Complete asymptotic analysis of low energy scattering for Schrödinger operators with a short-range potential","authors":"Ethan Sussman","doi":"10.1016/j.jfa.2026.111345","DOIUrl":"10.1016/j.jfa.2026.111345","url":null,"abstract":"<div><div>Recent work by Hintz–Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schrödinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic analysis by providing full asymptotic expansions in every possible asymptotic regime. Moreover, the analysis is done in any dimension <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, for any asymptotically conic manifold, and we keep track of partial multipole expansions. Applications include full asymptotic analyses of the Schrödinger, wave, and Klein–Gordon equations, one of these being described in a companion paper. Using previous work, only partial asymptotic analyses were possible.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111345"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036483","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 : 2026-04-15Epub 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":"2026-04-15","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 : 2026-04-15Epub Date: 2026-01-21DOI: 10.1016/j.jfa.2026.111349
Dolapo Oyetunbi, Dilian Yang
The 2-adic ring -algebra is the universal -algebra generated by a unitary and an isometry satisfying certain relations. It contains a canonical copy of the Cuntz algebra . We show that is a maximal -subalgebra of . Furthermore, we examine the structure of the fixed-point algebra under a periodic ⁎-automorphism σ of , which is extended from the flip-flop ⁎-automorphism of . We show that the maximality of in extends to the crossed product in , and to the fixed-point algebra in . As a consequences of our main results, a few open questions concerning are resolved.
二进环C -代数Q2是由满足一定关系的酉和等距生成的全称C -代数。它包含了昆兹代数O2的一个规范副本。我们证明O2是Q2的一个极大C - C -子代数。进一步，我们研究了由O2的触发器式的自同构推广而来的Q2的周期式的 -自同构σ下的不动点代数的结构。我们证明了Q2中O2的极大值可以扩展到Q2中O2的交叉积O2的∑z2，以及Q2中O2的不动代数O2的不动代数。由于我们的主要结果，一些关于Q2的开放问题得到了解决。
{"title":"Maximality and symmetry related to the 2-adic ring C⁎-algebra","authors":"Dolapo Oyetunbi, Dilian Yang","doi":"10.1016/j.jfa.2026.111349","DOIUrl":"10.1016/j.jfa.2026.111349","url":null,"abstract":"<div><div>The 2-adic ring <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> is the universal <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra generated by a unitary and an isometry satisfying certain relations. It contains a canonical copy of the Cuntz algebra <span><math><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. We show that <span><math><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> is a maximal <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-subalgebra of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. Furthermore, we examine the structure of the fixed-point algebra under a periodic <sup>⁎</sup>-automorphism <em>σ</em> of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, which is extended from the flip-flop <sup>⁎</sup>-automorphism of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. We show that the maximality of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> extends to the crossed product <span><math><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mo>⋊</mo></mrow><mrow><mi>σ</mi></mrow></msub><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mo>⋊</mo></mrow><mrow><mi>σ</mi></mrow></msub><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and to the fixed-point algebra <span><math><msubsup><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>σ</mi></mrow></msubsup></math></span> in <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>σ</mi></mrow></msubsup></math></span>. As a consequences of our main results, a few open questions concerning <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are resolved.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111349"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074899","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 : 2026-04-01Epub Date: 2025-12-19DOI: 10.1016/j.jfa.2025.111315
Yu Gu, Ran Tao
We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. Utilizing this identity, we obtain estimates for the polymer endpoints, leading to optimal fluctuation exponents for the height function in both the subcritical and critical regimes, as well as an optimal upper bound for the fluctuation exponents in the extended critical regime. We also compute the average growth rate as a function of the boundary parameter.
{"title":"Fluctuation exponents of the half-space KPZ at stationarity","authors":"Yu Gu, Ran Tao","doi":"10.1016/j.jfa.2025.111315","DOIUrl":"10.1016/j.jfa.2025.111315","url":null,"abstract":"<div><div>We study the half-space KPZ equation with a Neumann boundary condition, starting from stationary Brownian initial data. We derive a variance identity that links the fluctuations of the height function to the transversal fluctuations of a half-space polymer model. Utilizing this identity, we obtain estimates for the polymer endpoints, leading to optimal fluctuation exponents for the height function in both the subcritical and critical regimes, as well as an optimal upper bound for the fluctuation exponents in the extended critical regime. We also compute the average growth rate as a function of the boundary parameter.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111315"},"PeriodicalIF":1.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-12-19DOI: 10.1016/j.jfa.2025.111316
Jordy Timo van Velthoven , Felix Voigtlaender
We provide a characterization of two expansive dilation matrices yielding equal discrete anisotropic Triebel-Lizorkin spaces. For two such matrices A and B, and arbitrary and , it is shown that if and only if the set is finite, or in the trivial case when and . This provides an extension of a result by Triebel for diagonal dilations to arbitrary expansive matrices. The obtained classification of dilations is different from corresponding results for anisotropic Triebel-Lizorkin function spaces.
{"title":"Discrete Triebel-Lizorkin spaces and expansive matrices","authors":"Jordy Timo van Velthoven , Felix Voigtlaender","doi":"10.1016/j.jfa.2025.111316","DOIUrl":"10.1016/j.jfa.2025.111316","url":null,"abstract":"<div><div>We provide a characterization of two expansive dilation matrices yielding equal discrete anisotropic Triebel-Lizorkin spaces. For two such matrices <em>A</em> and <em>B</em>, and arbitrary <span><math><mi>α</mi><mo>∈</mo><mi>R</mi></math></span> and <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span>, it is shown that <span><math><msubsup><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mo>(</mo><mi>B</mi><mo>)</mo></math></span> if and only if the set <span><math><mo>{</mo><msup><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow></msup><msup><mrow><mi>B</mi></mrow><mrow><mo>−</mo><mi>j</mi></mrow></msup><mo>:</mo><mi>j</mi><mo>∈</mo><mi>Z</mi><mo>}</mo></math></span> is finite, or in the trivial case when <span><math><mo>|</mo><mi>det</mi><mo></mo><mo>(</mo><mi>A</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>p</mi></mrow></msup><mo>=</mo><mo>|</mo><mi>det</mi><mo></mo><mo>(</mo><mi>B</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>p</mi></mrow></msup></math></span> and <span><math><mi>p</mi><mo>=</mo><mi>q</mi></math></span>. This provides an extension of a result by Triebel for diagonal dilations to arbitrary expansive matrices. The obtained classification of dilations is different from corresponding results for anisotropic Triebel-Lizorkin function spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111316"},"PeriodicalIF":1.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-12-12DOI: 10.1016/j.jfa.2025.111314
Elias Hess-Childs , Renaud Raquépas , Keefer Rowan
We show that bounded divergence-free vector fields decrease (that is, do not increase) the “concentration”—quantified by the modulus of absolute continuity with respect to the Lebesgue measure—of solutions to the associated advection-diffusion equation when compared to solutions to the heat equation. In particular, for symmetric decreasing initial data, the solution to the advection-diffusion equation has (without a prefactor constant) larger variance, larger entropy, and smaller norms for all than the solution to the heat equation. We also note that the same is not true on .
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