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The author would like to express his gratitude to the anonymous referees for several suggestions throughout the text that led to improving the quality of the paper.

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Almost diagonalization theorem and global wave front sets in ultradifferentiable classes

Publicat a:Banach Journal Of Mathematical Analysis. 18 (4): 67- - 2024-10-01 18(4), DOI: 10.1007/s43037-024-00374-6

Autors: Asensio, Vicente

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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}$$aw(x,D)u$$\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.

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