Journal of Functional Analysis最新文献

Anderson localization for CMV matrices with Verblunsky coefficients defined by the hyperbolic toral automorphism 由双曲总自同构定义的具有Verblunsky系数的CMV矩阵的Anderson定位

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-19 DOI: 10.1016/j.jfa.2025.111103

Yanxue Lin , Shuzheng Guo , Daxiong Piao

引用次数: 0

Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction 具有奇异相互作用的无限多粒子非线性Hartree方程的全局适定性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111102

Sonae Hadama , Younghun Hong

引用次数: 0

Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms 一类Sobolev范数和BV范数的非局部近似的极限估计

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111106

Massimo Gobbino, Nicola Picenni

引用次数: 0

Calculus for parametric boundary problems with global projection conditions 具有全局投影条件的参数边界问题的微积分

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111099

Jörg Seiler

引用次数: 0

Non existence and strong ill-posedness in H2 for the stable IPM equation 稳定IPM方程在H2中的不存在性和强病态性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111097

Roberta Bianchini , Diego Córdoba , Luis Martínez-Zoroa

{"title":"Non existence and strong ill-posedness in H2 for the stable IPM equation","authors":"Roberta Bianchini , Diego Córdoba , Luis Martínez-Zoroa","doi":"10.1016/j.jfa.2025.111097","DOIUrl":"10.1016/j.jfa.2025.111097","url":null,"abstract":"<div><div>We prove the non-existence and strong ill-posedness of the Incompressible Porous Media (IPM) equation for initial data that are small <math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> perturbations of the linearly stable profile <math><mo>−</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></math>. A remarkable novelty of the proof is the construction of an <math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math> perturbation, which solves the IPM equation and neutralizes the stabilizing effect of the background profile near the origin, where a strong deformation leading to non-existence in <math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math> is created. This strong deformation is achieved through an iterative procedure inspired by the work of Córdoba and Martínez-Zoroa (2022) [7]. However, several differences - beyond purely technical aspects - arise due to the anisotropic and, more importantly, to the partially dissipative nature of the equation, adding further challenges to the analysis.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111097"},"PeriodicalIF":1.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489468","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}

引用次数: 0

On the mean-field and semiclassical limit from quantum N-body dynamics 量子n体动力学的平均场和半经典极限

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111100

Xuwen Chen , Shunlin Shen , Zhifei Zhang

{"title":"On the mean-field and semiclassical limit from quantum N-body dynamics","authors":"Xuwen Chen , Shunlin Shen , Zhifei Zhang","doi":"10.1016/j.jfa.2025.111100","DOIUrl":"10.1016/j.jfa.2025.111100","url":null,"abstract":"<div><div>We study the mean-field and semiclassical limit of the quantum many-body bosonic dynamics with a repulsive δ-type potential <math><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn><mi>β</mi></mrow></msup><mi>V</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>β</mi></mrow></msup><mi>x</mi><mo>)</mo></math> and a repulsive Coulomb potential on <math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math>, which leads to a macroscopic fluid equation, the Euler-Poisson equation with pressure. We prove quantitative strong convergence of the quantum mass and momentum densities up to the first blow up time of the limiting equation. The proof is based on a modulated energy method, for which a functional inequality is the key ingredient. Different from Golse-Paul [38] in which the sole Coulomb potential case was considered and one could use Serfaty's inequality [64], the δ-type potential's sharp singularity and general profile hinder the application of such inequalities. In this paper, we develop a completely new method, in which Erdős-Schlein-Yau [31], [33], [34] <math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math>-type energy estimate plays an unexpected role, to establish the functional inequality on the δ-type potential for the optimal case <math><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111100"},"PeriodicalIF":1.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144514337","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}

引用次数: 0

Asymptotic behaviour of semigroup traces and Schatten classes of resolvents 解的半群迹和Schatten类的渐近性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111101

Bruno Iochum , Valentin A. Zagrebnov

引用次数: 0

Derivation of renormalized Hartree-Fock-Bogoliubov and quantum Boltzmann equations in an interacting Bose gas 相互作用玻色气体中重整化Hartree-Fock-Bogoliubov方程和量子玻尔兹曼方程的推导

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111096

Thomas Chen , Michael Hott

{"title":"Derivation of renormalized Hartree-Fock-Bogoliubov and quantum Boltzmann equations in an interacting Bose gas","authors":"Thomas Chen , Michael Hott","doi":"10.1016/j.jfa.2025.111096","DOIUrl":"10.1016/j.jfa.2025.111096","url":null,"abstract":"<div><div>Our previous work [37] presented a rigorous derivation of quantum Boltzmann equations near a Bose-Einstein condensate (BEC). Here, we extend it with a complete characterization of the leading order fluctuation dynamics. For this purpose, we correct the latter via an appropriate Bogoliubov rotation, in partial analogy to the approach by Grillakis-Machedon et al. [60], in addition to the Weyl transformation applied in [37]. Based on the analysis of the third order expansion of the BEC wave function, and the second order expansions of the pair-correlations, we show that through a renormalization strategy, various contributions to the effective Hamiltonian can be iteratively eliminated by an appropriate choice of the Weyl and Bogoliubov transformations. This leads to a separation of renormalized Hartree-Fock-Bogoliubov (HFB) equations and quantum Boltzmann equations. A multitude of terms that were included in the error term in [37] is now identified as contributions to the HFB renormalization terms. Thereby, the error bound in the work at hand is improved significantly. To the given order, it is now sharp, and matches the order or magnitude expected from scaling considerations. Consequently, we extend the time of validity to <math><mi>t</mi><mo>∼</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>N</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math> compared to <math><mi>t</mi><mo>∼</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>N</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>N</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math> before. We expect our approach to be extensible to smaller orders in <math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac></math>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111096"},"PeriodicalIF":1.7,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338324","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}

引用次数: 0

Solvability for the Ginzburg-Landau equation linearized at the degree-one vortex 一级涡线性化的金兹堡-朗道方程的可解性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-18 DOI: 10.1016/j.jfa.2025.111105

Manuel del Pino, Rowan Juneman, Monica Musso

引用次数: 0

Restrictions of pure states to subspaces of C⁎-algebras C -代数的纯态对子空间的限制

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-06-17 DOI: 10.1016/j.jfa.2025.111104

Raphaël Clouâtre

{"title":"Restrictions of pure states to subspaces of C⁎-algebras","authors":"Raphaël Clouâtre","doi":"10.1016/j.jfa.2025.111104","DOIUrl":"10.1016/j.jfa.2025.111104","url":null,"abstract":"<div><div>Given a unital subspace M of a <math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>-algebra B, the fundamental problem that we consider is to describe those pure states ω on B for which <math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub><mo>=</mo><mo>{</mo><mi>ω</mi><mo>}</mo></math>, where <math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub></math> is the set of states on B extending <math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math>. In other words, we aim to understand when <math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math> admits a unique extension to a state on B. We find that the obvious necessary condition that <math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math> also be pure is sufficient in some naturally occurring examples, but not in general. Guided by classical results for spaces of continuous functions, we then turn to noncommutative peaking phenomena, and to several variations on noncommutative peak points that have previously appeared in the literature. We illustrate that all of them are in fact distinct, address their existence and, in some cases, their relative abundance. To solve our main problem, we introduce a new type of peaking behaviour for ω, namely that the set <math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub></math> be what we call an M-pinnacle set. Roughly speaking, our main result is that <math><mi>ω</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>M</mi></mrow></msub></math> admits a unique extension to B if and only if <math><msub><mrow><mi>E</mi></mrow><mrow><mi>ω</mi></mrow></msub></math> is an M-pinnacle set.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111104"},"PeriodicalIF":1.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491152","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}

引用次数: 0