Pseudodifferential operators with rough negative definite symbols
type: Item
instance of: scholarly article
title: Pseudodifferential operators with rough negative definite symbols
zbMATH Open document ID: 1207.47049
author: Alexander Potrykus
published in: Integral Equations and Operator Theory
publication date: 2010-08-23T00:00:00Z
review text: The author studies pseudodifferential operators with negative definite symbols \(p(x,\xi )\) with minimal assumptions regarding their smoothness in \(\xi\). He proves an asymptotic expansion formula for the composition of such operators and finds new conditions under which a pseudodifferential operator of the above type generates a Feller semigroup. The latter is found possible for a class of symbols which are only continuous in \(\xi\). The smoothness conditions with respect to \(x\) are also improved compared to earlier results in this direction [see \textit{N.\,Jacob}, Forum Math.\ 4, No.\,5, 433--446 (1992; Zbl 0759.60078); \textit{W.\,Hoh}, Stochastics Stochastics Rep.\ 55, No.\, 3--4, 225--252 (1995; Zbl 0880.47029)]. The technique builds on a method by \textit{O.\,A.\thinspace Olejnik} and \textit{E.\,V.\thinspace Radkevich} [Itogi Nauki, Ser.\,Mat., Mat.\ Analiz 1969 (1971; Zbl 0217.41502)].
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 5774256
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: rough symbols
zbMATH Keywords: symbolic calculus
zbMATH Keywords: Feller semigroups
zbMATH Keywords: asymptotic expansions
MaRDI profile type: Publication
full work available at URL: s00020-010-1755-1
OpenAlex ID: W2043301426
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DOI: 10.1007/S00020-010-1755-1
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description: scientific article; zbMATH DE number 5774256