The pseudoanalytic extension
type: Item
instance of: scholarly article
title: The pseudoanalytic extension
zbMATH Open document ID: 0795.30034
DOI: 10.1007/BF03341966
published in: Journal d'Analyse Mathématique
publication date: 1994-09-01T00:00:00Z
review text: The paper under review is a survey. The main technique is a description of smooth functions in terms of the so-called analytic continuation. The idea of pseudoanalytic continuation was developed by the author. Roughly speaking the approach of pseudoanalytic continuation describes classes of various smooth functions as functions which admit a continuation to a neighbourhood of their domain such that the \(\overline\partial\) derivative is small near the boundary. This approach is shown to be very powerful. The author describes many classes of functions in terms of pseudoanalytic continuation: Hölder classes, Sobolev classes, Besov classes, Carleman classes. In the survey under review the author demonstrates the technique of pseudoanalytic continuation by solving several problems or giving new proofs: Denjoy-Carleman theorem, interpolation problems in spaces of smooth functions, multipliers properties of inner functions on Hölder classes, and others. The paper is written very clearly.
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 26E10
zbMATH DE Number: 528687
zbMATH Keywords: Sobolev classes
zbMATH Keywords: Besove classes
zbMATH Keywords: Carleman classes
zbMATH Keywords: pseudoanalytic continuation
author: Evsey Dyn'kin
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03341966
OpenAlex ID: W1970231522
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description: scientific article; zbMATH DE number 528687