Almost diagonalization theorem and global wave front sets in ultradifferentiable classes

被引:1
作者
Asensio, Vicente [1 ,2 ]
机构
[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA, Camino Vera,s-n, Valencia 46022, Spain
[2] Ctr Univ EDEM, Placa Aigua,s-n, Valencia 46024, Spain
关键词
Global wave front set; Almost diagonalization; Global ultradifferentiable classes; Gabor frames; PARTIAL-DIFFERENTIAL OPERATORS; PSEUDODIFFERENTIAL-OPERATORS; INFINITE-ORDER; SPACES;
D O I
10.1007/s43037-024-00374-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main aim of this paper is to prove that the wave front set of aw(x,D)u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a<^>w(x,D)u$$\end{document}, i.e. the action of the Weyl operator with symbol a on u, is contained in the wave front set of u and in the conic support of a in spaces of omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-tempered ultradistributions in the Beurling setting for adequate symbols of ultradifferentiable type. These symbols are not restricted to have order zero. To do so, we prove an almost diagonalization theorem on Weyl operators. Furthermore, an almost diagonalization theorem involving time-frequency analysis leads to additional applications, such as invertibility of pseudodifferential operators or boundedness of them in modulation spaces with exponential growth.
引用
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页数:29
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