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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.

Analysis of institutional authors

Asensio, VicenteCorresponding Author

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October 10, 2024
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Almost diagonalization theorem and global wave front sets in ultradifferentiable classes

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

Authors: Asensio, Vicente

Affiliations

Ctr Univ EDEM, Placa Aigua,s-n, Valencia 46024, Spain - Author
Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA, Camino Vera,s-n, Valencia 46022, Spain - Author

Abstract

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.

Keywords

Almost diagonalizationGabor frameGlobal ultradifferentiable classesGlobal wave front setInfinite-orderPartial-differential operatorsPseudodifferential-operatorsSpace

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Banach Journal Of Mathematical Analysis due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 108/483, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-09-07:

  • WoS: 1

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Asensio López, Vicente) and Last Author (Asensio López, Vicente).

the author responsible for correspondence tasks has been Asensio López, Vicente.