文献类型：期刊文献

英文题名：Cyclic vectors in Fock-type spaces in multi-variable case

作者：Huang, Hansong[1];Izuchi, Kou Hei[2]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Yamaguchi Univ, Dept Math Educ, Yamaguchi 7538511, Japan

年份：2024

卷号：15

期号：2

外文期刊名：ANNALS OF FUNCTIONAL ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001163945300001)】；

基金：This work was completed with the support of NSFC (12071134).

语种：英文

外文关键词：Cyclic vectors; Fock-type spaces; Multi-variable case

摘要：This manuscript concerns with cyclic vectors in the Fock-type spaces Lap(Cd,s,alpha)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L<^>{p}_{a}}(\mathbb C<^>d,s,\alpha )$$\end{document} of multi-variable cases, with positive parameters s,alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s,\alpha $$\end{document} and p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\ge 1$$\end{document}. The one-variable case has been settled by the authors. Here, it is shown that for a positive number s is not an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s\not \in \mathbb {N}$$\end{document}, a function f in the Fock-type space Lap(Cd,s,alpha)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L<^>{p}_{a}}(\mathbb C<^>d,s,\alpha )$$\end{document} is cyclic if and only if f is non-vanishing. However, the case of s being a positive integer turns out to be more complicated. Different techniques and methods are developed in multi-variable cases for a complete characterization of cyclic vectors in Lap(Cd,s,alpha)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L<^>{p}_{a}}(\mathbb C<^>d,s,\alpha )$$\end{document} for positive integers s.