Inhomogeneous Gevrey classes and ultradistributions
type: Item
instance of: scholarly article
title: Inhomogeneous Gevrey classes and ultradistributions
zbMATH Open document ID: 1065.46026
author: Daniela Calvo
author: Alessandro Morando
author: Luigi Rodino
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-10-12T00:00:00Z
review text: Starting from the definition of inhomogeneous Gevrey classes given by \textit{O. Liess} and \textit{L. Rodino} [Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 3, 233--323 (1984; Zbl 0557.35131)], the authors introduce the non-quasi-analytic inhomogeneous Gevrey classes of Roumieu type, denoted by \(G^{s, \lambda}.\) Such a class of ultradifferentiable functions is always between two standard Gevrey classes, and therefore contains non-trivial functions with compact support. \(G^{s, \lambda}\) need not be an algebra under pointwise multiplication, except in the case that the function \(\lambda\) satisfies the ring condition. The lack of the ring condition is fundamental in order to include the study the multianisotropic Gevrey classes. Topological properties of these spaces are studied and dual spaces are introduced. Under the Fourier-Laplace transform, the dual of \(G^{s, \lambda}\) is isomorphic to a weighted LF-space of entire functions.
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46F12
zbMATH DE Number: 2107217
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.043
OpenAlex ID: W2069736765
cites work: Ultradifferentiable functions and Fourier analysis
cites work: Linear partial differential operators and generalized distributions
cites work: Gevrey vectors of multi-quasi-elliptic systems
cites work: Q5428746
cites work: Q3620496
cites work: Complementi alla mia nota: su una classe di polinomi ipoellittici
cites work: Q3733286
cites work: Q5545711
cites work: Q4202964
cites work: Gevrey class solutions of hypoelliptic equations
cites work: Q5518756
cites work: Projective and injective limits of weakly compact sequences of locally convex spaces
cites work: Q5673937
cites work: Intersection properties of weak analytically uniform classes of functions
cites work: Q3222656
cites work: Q5593959
cites work: Q5814065
cites work: Theory of pseudo-differential operators of ultradifferentiable class
cites work: Q4722576
cites work: Q4274290
cites work: Sur quelques extensions de la notion de distribution
cites work: Q5597802
cites work: Q5848488
cites work: Q5557339
cites work: Q3892628
cites work: Q3934866
DOI: 10.1016/J.JMAA.2004.04.043
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description: scientific article; zbMATH DE number 2107217