Non-quasianalytic curves in Fréchet spaces
type: Item
instance of: scholarly article
title: Non-quasianalytic curves in Fréchet spaces
zbMATH Open document ID: 1246.46038
author: Jordi Juan-Huguet
published in: Monatshefte für Mathematik
publication date: 2011-12-14T00:00:00Z
review text: The author studies non-quasianalytic curves in locally convex spaces, i.e., vector valued \(\omega\)-ultradifferentiable functions \(f:\Omega\to E\) in the setting given by [\textit{R. W. Braun, R. Meise} and \textit{B. A. Taylor}, ``Ultradifferentiable functions and Fourier analysis'', Result. Math. 17, No. 3--4, 206--237 (1990; Zbl 0735.46022)], where \(\Omega\) is an open subset of \(\mathbb{R}^n\) and \(E\) is a locally convex space. In 1990, \textit{A. Kriegl} and \textit{P. W. Michor} [``The convenient setting for real analytic mappings'', Acta Math. 165, No. 1--2, 105--159 (1990; Zbl 0738.46024)] introduced several notions of real analytic curves in a locally convex space \(E\). Since 1998, Bonet and Domański have investigated in different papers real analytic curves with values in Fréchet and (LB)-spaces, clarifying the relation between various notions of real analyticity introduced by Kriegl and Michor (see, for example, [\textit{J. Bonet} and \textit{P. Domański}, ``Real analytic curves in Fréchet spaces and their duals'', Monatsh. Math. 126, No. 1, 13--36 (1998; Zbl 0918.46034)]), and have applied their results to investigate surjective linear partial differential operators between spaces of vector valued real analytic functions and parameter dependence of the solutions of these operators. The author solves a problem posed by Kriegl and Michor in a meeting celebrated in Paderborn (Germany) in November 2008 with the characterization of different notions of non-quasianalytic curves which take values in a Fréchet or (LB)-space.
reviewed by: David Jornet
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A63
zbMATH DE Number: 5988483
zbMATH Keywords: non-quasianalytic classes
zbMATH Keywords: vector valued ultradifferentiable functions
zbMATH Keywords: Fréchet spaces
zbMATH Keywords: property (DN)
MaRDI profile type: Publication
full work available at URL: s00605-010-0243-7
OpenAlex ID: W41628597
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DOI: 10.1007/S00605-010-0243-7
description: scientific article; zbMATH DE number 5988483