arXiv - MATH - Functional Analysis最新文献_第5页

Hankel operators and Projective Hilbert modules on quotients of bounded symmetric domains 有界对称域商上的汉克尔算子和投影希尔伯特模块

arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI: arxiv-2409.04582

Tirthankar Bhattacharyya, Mainak Bhowmik, Haripada Sau

{"title":"Hankel operators and Projective Hilbert modules on quotients of bounded symmetric domains","authors":"Tirthankar Bhattacharyya, Mainak Bhowmik, Haripada Sau","doi":"arxiv-2409.04582","DOIUrl":"https://doi.org/arxiv-2409.04582","url":null,"abstract":"Consider a bounded symmetric domain $Omega$ with a finite pseudo-reflection\u0000group acting on it as a subgroup of the group of automorphisms. This gives rise\u0000to quotient domains by means of basic polynomials $theta$ which by virtue of\u0000being proper maps map the v Silov boundary of $Omega$ to the v Silov\u0000boundary of $theta(Omega)$. Thus, the natural measure on the v Silov\u0000boundary of $Omega$ can be pushed forward. This gives rise to Hardy spaces on\u0000the quotient domain. The study of Hankel operators on the Hardy spaces of the quotient domains is\u0000introduced. The use of the weak product space shows that an analogue of\u0000Hartman's theorem holds for the small Hankel operator. Nehari's theorem fails\u0000for the big Hankel operator and this has the consequence that when the domain\u0000$Omega$ is the polydisc $mathbb D^d$, the {em Hardy space} is not a\u0000projective object in the category of all Hilbert modules over the algebra\u0000$mathcal A (theta(mathbb D^d))$ of functions which are holomorphic in the\u0000quotient domain and continuous on the closure $overline {theta(mathbb\u0000D^d)}$. It is not a projective object in the category of cramped Hilbert\u0000modules either. Indeed, no projective object is known in these two categories.\u0000On the other hand, every normal Hilbert module over the algebra of continuous\u0000functions on the v Silov boundary, treated as a Hilbert module over the\u0000algebra $mathcal A (theta(mathbb D^d))$, is projective.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The essential norms of Toeplitz operators with symbols in $C+H^infty$ on weighted Hardy spaces are independent of the weights 加权哈代空间上符号为 $C+H^infty$ 的托普利兹算子的基本规范与权重无关

arXiv - MATH - Functional Analysis Pub Date : 2024-09-05 DOI: arxiv-2409.03548

Oleksiy Karlovych, Eugene Shargorodsky

引用次数: 0

Shift invariant subspaces of large index in the Bloch space 布洛赫空间中的大索引位移不变子空间

arXiv - MATH - Functional Analysis Pub Date : 2024-09-05 DOI: arxiv-2409.03562

Nikiforos Biehler

引用次数: 0

Global bifurcation of homoclinic solutions 同轴解的全局分岔

arXiv - MATH - Functional Analysis Pub Date : 2024-09-05 DOI: arxiv-2409.03851

Iacopo P. Longo, Christian Pötzsche, Robert Skiba

引用次数: 0

Parallel methods for quasinonexpansive mappings in a Hilbert space 希尔伯特空间中准无穷映射的并行方法

arXiv - MATH - Functional Analysis Pub Date : 2024-09-05 DOI: arxiv-2409.03242

Koji Aoyama, Shigeru Iemoto

引用次数: 0

Admissibility Conditions for Multi-window Gabor Frames on Discrete Periodic Sets 离散周期集上多窗口 Gabor 帧的可接受性条件

arXiv - MATH - Functional Analysis Pub Date : 2024-09-05 DOI: arxiv-2409.03423

Najib Khachiaa, Mohamed Rossafi

引用次数: 0

On a doubly sublinear fractional $p$-Laplacian equation 关于一个双次线性分数 $p$-Laplacian 方程

arXiv - MATH - Functional Analysis Pub Date : 2024-09-05 DOI: arxiv-2409.03616

A. Iannizzotto, S. Mosconi

引用次数: 0

Paired kernels and truncated Toeplitz operators 成对核与截断托普利兹算子

arXiv - MATH - Functional Analysis Pub Date : 2024-09-04 DOI: arxiv-2409.02563

M. Cristina Câmara, Jonathan R. Partington

引用次数: 0

Some extensions from famous theorems for $h$-mid-convex function $h$中凸函数著名定理的一些扩展

arXiv - MATH - Functional Analysis Pub Date : 2024-09-04 DOI: arxiv-2409.02450

Amir Garejelo, Farzollah Mirzapour, Ali Morassaei

引用次数: 0

A sparse resolution of the DiPerna-Majda gap problem for $2$D Euler equations 2$D 欧拉方程的 DiPerna-Majda 缺口问题的稀疏解决方案

arXiv - MATH - Functional Analysis Pub Date : 2024-09-04 DOI: arxiv-2409.02344

Oscar Domínguez, Daniel Spector

{"title":"A sparse resolution of the DiPerna-Majda gap problem for $2$D Euler equations","authors":"Oscar Domínguez, Daniel Spector","doi":"arxiv-2409.02344","DOIUrl":"https://doi.org/arxiv-2409.02344","url":null,"abstract":"A central question which originates in the celebrated work in the 1980's of\u0000DiPerna and Majda asks what is the optimal decay $f > 0$ such that uniform\u0000rates $|omega|(Q) leq f(|Q|)$ of the vorticity maximal functions guarantee\u0000strong convergence without concentrations of approximate solutions to\u0000energy-conserving weak solutions of the $2$D Euler equations with vortex sheet\u0000initial data. A famous result of Majda (1993) shows $f(r) = [log\u0000(1/r)]^{-1/2}$, $r<1/2$, as the optimal decay for emph{distinguished} sign\u0000vortex sheets. In the general setting of emph{mixed} sign vortex sheets,\u0000DiPerna and Majda (1987) established $f(r) = [log (1/r)]^{-alpha}$ with\u0000$alpha > 1$ as a sufficient condition for the lack of concentrations, while\u0000the expected gap $alpha in (1/2, 1]$ remains as an open question. In this\u0000paper we resolve the DiPerna-Majda $2$D gap problem: In striking contrast to\u0000the well-known case of distinguished sign vortex sheets, we identify $f(r) =\u0000[log (1/r)]^{-1}$ as the optimal regularity for mixed sign vortex sheets that\u0000rules out concentrations. For the proof, we propose a novel method to construct explicitly solutions\u0000with mixed sign to the $2$D Euler equations in such a way that wild behaviour\u0000creates within the relevant geometry of emph{sparse} cubes (i.e., these cubes\u0000are not necessarily pairwise disjoint, but their possible overlappings can be\u0000controlled in a sharp fashion). Such a strategy is inspired by the recent work\u0000of the first author and Milman cite{DM} where strong connections between\u0000energy conservation and sparseness are established.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0