Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in der \(L^ p\)-Theorie. (The spectral invariance of algebras of pseudodifferential operators in the \(L^ p\)-theory)
type: Item
instance of: scholarly article
title: Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in der \(L^ p\)-Theorie. (The spectral invariance of algebras of pseudodifferential operators in the \(L^ p\)-theory)
zbMATH Open document ID: 0674.47033
DOI: 10.1007/BF01258600
author: Johannes Ueberberg
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155326
review text: Let \(\Psi^ 0_{1,\delta}(0\leq \delta <1)\) be the Hörmander class of pseudodifferential operators. It is shown that if an operator P from \(\Psi^ 0_{1,\delta}\) is invertible in \({\mathfrak L}(L^ p({\mathbb{R}}^ n))\) then \(P^{-1}\in \Psi^ 0_{1,\delta}\). This statement means, in particular, that \(\Psi^ 0_{1,\delta}\) is a so-called \(\Psi\)-algebra in \({\mathfrak L}(L^ p({\mathbb{R}}^ n))\). The proof is based on methods developed earlier by R. Beals, R. R. Coifman, Y. Meyer and H. O. Cordes.
Mathematics Subject Classification ID: 47Gxx
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 46K05
zbMATH DE Number: 4103801
zbMATH Keywords: Hörmander class of pseudodifferential operators
zbMATH Keywords: \(\Psi\)-algebra
reviewed by: Józef Banaś
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4103801