arXiv - MATH - Functional Analysis最新文献_第9页

Differential equations defined by Kreĭn-Feller operators on Riemannian manifolds 黎曼流形上 Kreĭn-Feller 算子定义的微分方程

arXiv - MATH - Functional Analysis Pub Date : 2024-08-09 DOI: arxiv-2408.04858

Sze-Man Ngai, Lei Ouyang

引用次数: 0

A regularity condition under which integral operators with operator-valued kernels are trace class 具有算子值核的积分算子是迹类的正则条件

arXiv - MATH - Functional Analysis Pub Date : 2024-08-09 DOI: arxiv-2408.04794

John Zweck, Yuri Latushkin, Erika Gallo

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An Exposition on Weak Stability of Operators 关于算子弱稳定性的阐述

arXiv - MATH - Functional Analysis Pub Date : 2024-08-08 DOI: arxiv-2408.04186

C. S. Kubrusly

引用次数: 0

Monotonicity properties of weighted geometric symmetrizations 加权几何对称的单调性特性

arXiv - MATH - Functional Analysis Pub Date : 2024-08-08 DOI: arxiv-2408.04357

Katarina Bogdanović, Aljoša Peperko

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Poincaré's lemma for formal manifolds 形式流形的泊恩卡雷定理

arXiv - MATH - Functional Analysis Pub Date : 2024-08-08 DOI: arxiv-2408.04263

Fulin Chen, Binyong Sun, Chuyun Wang

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A transference principle for involution-invariant functional Hilbert spaces 内卷不变函数希尔伯特空间的转移原理

arXiv - MATH - Functional Analysis Pub Date : 2024-08-08 DOI: arxiv-2408.04384

Santu Bera, Sameer Chavan, Shubham Jain

{"title":"A transference principle for involution-invariant functional Hilbert spaces","authors":"Santu Bera, Sameer Chavan, Shubham Jain","doi":"arxiv-2408.04384","DOIUrl":"https://doi.org/arxiv-2408.04384","url":null,"abstract":"Let $sigma : mathbb C^d rightarrow mathbb C^d$ be an affine-linear\u0000involution such that $J_sigma = -1$ and let $U, V$ be two domains in $mathbb\u0000C^d$ with $U$ being $sigma$-invariant. Let $phi : U rightarrow V$ be a\u0000$sigma$-invariant $2$-proper map such that $J_phi$ is affine-linear and let\u0000$mathscr H(U)$ be a $sigma$-invariant reproducing kernel Hilbert space of\u0000complex-valued holomorphic functions on $U.$ It is shown that the space\u0000$mathscr H_phi(V):={f in mathrm{Hol}(V) : J_phi cdot f circ phi in\u0000mathscr H(U)}$ endowed with the norm $|f|_phi :=|J_phi cdot f circ\u0000phi|_{mathscr H(U)}$ is a reproducing kernel Hilbert space and the linear\u0000mapping $varGamma_phi$ defined by $ varGamma_phi(f) = J_phi cdot f circ\u0000phi,$ $f in mathrm{Hol}(V),$ is a unitary from $mathscr H_phi(V)$ onto\u0000${f in mathscr H(U) : f = -f circ sigma}.$ Moreover, a neat formula for\u0000the reproducing kernel $kappa_{phi}$ of $mathscr H_phi(V)$ in terms of the\u0000reproducing kernel of $mathscr H(U)$ is given. The above scheme is applicable\u0000to symmetrized bidisc, tetrablock, $d$-dimensional fat Hartogs triangle and\u0000$d$-dimensional egg domain. This recovers some known results. Our result not\u0000only yields a candidate for Hardy spaces but also an analog of von Neumann's\u0000inequality for contractive tuples naturally associated with these domains.\u0000Unlike the existing techniques, we capitalize on the methods from several\u0000complex variables.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930539","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

New variable weighted conditions for fractional maximal operators over spaces of homogeneous type 同质类型空间上分数最大算子的新变量加权条件

arXiv - MATH - Functional Analysis Pub Date : 2024-08-08 DOI: arxiv-2408.04544

Xi Cen

{"title":"New variable weighted conditions for fractional maximal operators over spaces of homogeneous type","authors":"Xi Cen","doi":"arxiv-2408.04544","DOIUrl":"https://doi.org/arxiv-2408.04544","url":null,"abstract":"Based on the rapid development of dyadic analysis and the theory of variable\u0000weighted function spaces over the spaces of homogeneous type $(X,d,mu)$ in\u0000recent years, we systematically consider the quantitative variable weighted\u0000characterizations for fractional maximal operators. On the one hand, a new\u0000class of variable multiple weight $A_{vec{p}(cdot),q(cdot)}(X)$ is\u0000established, which enables us to prove the strong and weak type variable\u0000multiple weighted estimates for multilinear fractional maximal operators\u0000${{{mathscr M}_{eta }}}$. More precisely, [ {left[ {vec omega }\u0000right]_{{A_{vec p( cdot ),q( cdot )}}(X)}} lesssim {left|\u0000mathscr{M}_eta right|_{prodlimits_{i = 1}^m {{L^{p_i( cdot )}}({X,omega\u0000_i})} to {L^{q( cdot )}}(X,omega )({WL^{q( cdot )}}(X,omega ))}} le\u0000{C_{vec omega ,eta ,m,mu ,X,vec p( cdot )}}. ] On the other hand, on account of the classical Sawyer's condition\u0000$S_{p,q}(mathbb{R}^n)$, a new variable testing condition\u0000$C_{{p}(cdot),q(cdot)}(X)$ also appears in here, which allows us to obtain\u0000quantitative two-weighted estimates for fractional maximal operators\u0000${{{M}_{eta }}}$. To be exact, begin{align*} |M_{eta}|_{L^{p(cdot)}(X,omega)rightarrow L^{q(cdot)}(X,v)} lesssim\u0000sum_{theta=frac{1}{{{p_{rm{ - }}}}},frac{1}{{{p_{rm{ + }}}}}}\u0000left([omega ]_{C_{p( cdot ),q( cdot )}^1(X)} [omega, v]_{C_{p(cdot),\u0000q(cdot)}^2(X)}right)^{theta}, end{align*} The implicit constants mentioned\u0000above are independent on the weights.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949475","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

Collective order convergence and collectively qualified set of operators 集体阶收敛和集体合格算子集

arXiv - MATH - Functional Analysis Pub Date : 2024-08-07 DOI: arxiv-2408.03671

Eduard Emelyanov

引用次数: 0

Gershgorin-Type Spectral Inclusions for Matrices 矩阵的格什高林型谱夹杂

arXiv - MATH - Functional Analysis Pub Date : 2024-08-07 DOI: arxiv-2408.03883

Simon N. Chandler-Wilde, Marko Lindner

引用次数: 0

Representations of the Möbius group and pairs of homogeneous operators in the Cowen-Douglas class 莫比乌斯群的表示和考文-道格拉斯类同质算子对

arXiv - MATH - Functional Analysis Pub Date : 2024-08-07 DOI: arxiv-2408.03711

Jyotirmay Das, Somnath Hazra

{"title":"Representations of the Möbius group and pairs of homogeneous operators in the Cowen-Douglas class","authors":"Jyotirmay Das, Somnath Hazra","doi":"arxiv-2408.03711","DOIUrl":"https://doi.org/arxiv-2408.03711","url":null,"abstract":"Let M\"ob be the biholomorphic automorphism group of the unit disc of the\u0000complex plane, $mathcal{H}$ be a complex separable Hilbert space and\u0000$mathcal{U}(mathcal{H})$ be the group of all unitary operators. Suppose\u0000$mathcal{H}$ is a reproducing kernel Hilbert space consisting of holomorphic\u0000functions over the poly-disc $mathbb D^n$ and contains all the polynomials. If\u0000$pi : mbox{M\"ob} to mathcal{U}(mathcal{H})$ is a multiplier\u0000representation, then we prove that there exist $lambda_1, lambda_2, ldots,\u0000lambda_n > 0$ such that $pi$ is unitarily equivalent to $(otimes_{i=1}^{n}\u0000D_{lambda_i}^+)|_{mbox{M\"ob}}$, where each $D_{lambda_i}^+$ is a\u0000holomorphic discrete series representation of M\"ob. As an application, we\u0000prove that if $(T_1, T_2)$ is a M\"ob - homogeneous pair in the Cowen - Douglas\u0000class of rank $1$ over the bi-disc, then each $T_i$ posses an upper triangular\u0000form with respect to a decomposition of the Hilbert space. In this upper\u0000triangular form of each $T_i$, the diagonal operators are identified. We also\u0000prove that if $mathcal{H}$ consists of symmetric (resp. anti-symmetric)\u0000holomorphic functions over $mathbb D^2$ and contains all the symmetric (resp.\u0000anti-symmetric) polynomials, then there exists $lambda > 0$ such that $pi\u0000cong oplus_{m = 0}^infty D^+_{lambda + 4m}$ (resp. $pi cong\u0000oplus_{m=0}^infty D^+_{lambda + 4m + 2}$).","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930555","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