Global wave front sets in ultradifferentiable classes
type: Item
instance of: scholarly article
title: Global wave front sets in ultradifferentiable classes
zbMATH Open document ID: 1487.35013
author: Vicente Asensio
author: Chiara Boiti
author: A. Oliaro
author: David Jornet
published in: Results in Mathematics
publication date: 2022-03-15T00:00:00Z
review text: The paper concerns global wave front sets of the type of those first considered by \textit{L. Hörmander} [Lect. Notes Math. 1495, 118--160 (1991; Zbl 0761.35004)] and subsequently in terms of short-time Fourier transform by \textit{L. Rodino} and \textit{P. Wahlberg} [Monatsh. Math. 173, No. 4, 625--655 (2014; Zbl 1366.42030)], under the name of Gabor wave front sets. Here attention is fixed on the global ultra-differentiable classes, defined as for example in [\textit{G. Björck}, Ark. Mat. 6, 351--407 (1966; Zbl 0166.36501)]. The corresponding microlocal regularity was already considered by \textit{C. Boiti} et al. [Monatsh. Math. 188, No. 2, 199--246 (2019; Zbl 1407.35003)]. In the present paper, taking advantage from the pseudo-differential calculus of \textit{V. Asensio} and \textit{D. Jornet} [Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 113, No. 4, 3477--3512 (2019; Zbl 1439.46028)], the authors give an equivalent definition and prove in this frame a result of micro-elliptic regularity. Note that the global ultra-differentiable setting involves severe technical difficulties and, on the other hand, it is very general including the Gelfand-Shilov spaces as a particular case.
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35A18
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35R50
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 7490176
zbMATH Keywords: Gabor wave front set
zbMATH Keywords: global ultradifferentiable classes
zbMATH Keywords: Gabor transform
MaRDI profile type: Publication
full work available at URL: s00025-021-01597-x
OpenAlex ID: W4210284215
cites work: Quasianalytic wave front sets for solutions of linear partial differential operators
cites work: Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes
cites work: Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions
cites work: Linear partial differential operators and generalized distributions
cites work: A simple proof of Kotake-Narasimhan theorem in some classes of ultradifferentiable functions
cites work: A characterization of the wave front set defined by the iterates of an operator with constant coefficients
cites work: Wave front sets with respect to the iterates of an operator with constant coefficients
cites work: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms
cites work: The Gabor wave front set in spaces of ultradifferentiable functions
cites work: Real Paley-Wiener theorems in spaces of ultradifferentiable functions
cites work: Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis
cites work: Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
cites work: Ultradifferentiable functions and Fourier analysis
cites work: Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions
cites work: Time-frequency analysis of localization operators.
cites work: Characterization of nuclearity for Beurling–Björck spaces
cites work: The nuclearity of Gelfand-Shilov spaces and kernel theorems
cites work: Superposition in classes of ultradifferentiable functions
cites work: \(\omega\)-hypoelliptic differential operators of constant strength
cites work: Pseudodifferential operators of Beurling type and the wave front set
cites work: Weight functions for classes of ultradifferentiable functions
cites work: Foundations of time-frequency analysis
cites work: Spaces of test functions via the STFT
cites work: Fourier integral operators. I
cites work: Q4016478
cites work: Q4349650
cites work: Propagation of the homogeneous wave front set for Schrödinger equations
cites work: Q5425073
cites work: Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions
cites work: Anti-Wick and Weyl quantization on ultradistribution spaces
cites work: Infinite order \(\Psi\mathrm{DOs}\): composition with entire functions, new Shubin-Sobolev spaces, and index theorem
cites work: Pseudodifferential operators of infinite order in spaces of tempered ultradistributions
cites work: Q4274290
cites work: The Gabor wave front set
cites work: Equality of the homogeneous and the Gabor wave front set
cites work: Q2736011
cites work: Q3037865
DOI: 10.1007/S00025-021-01597-X
description: scientific article; zbMATH DE number 7490176