Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in der \(L^ p\)-Theorie. (The spectral invariance of algebras of pseudodifferential operators in the \(L^ p\)-theory)
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.
Hörmander class of pseudodifferential operators
scientific article; zbMATH DE number 4103801
scientific article