Boundedness and spectral invariance for standard pseudodifferential operators on anisotropically weighted \(L^ p\)-Sobolev spaces

DOI10.1007/BF01193760zbMath0703.35186MaRDI QIDQ916010

Elmar Schrohe

Publication date: 1990

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

perturbation theorysymbolsspectral invarianceweighted \(L^ p\)-Sobolev space

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) General topics in linear spectral theory for PDEs (35P05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Ideals and subalgebras (46H10)

Related Items (15)

Spectral invariance for pseudodifferential operators on weighted function spaces ⋮ Adaptive Wavelet Computations for Inverses of Pseudo-Differential Operators ⋮ A characterization of the singular green operators in boutet de monvel's calculus via wedge sobolev spaces ⋮ Invariance of the Fredholm index and spectrum of non-smooth pseudodifferential operators ⋮ Spectral Invariance for Algebras of Pseudodifferential Operators on Besov Spaces of Variable Order of Differentiation ⋮ Fredholm and regularity theory of Douglis-Nirenberg elliptic systems on \({\mathbb{R}}^{N}\) ⋮ Spectral invariance for pseudodifferential operators in Hölder-Zygmund spaces of the variable smoothness ⋮ Invariance of the $L_p$ spectrum for hypoelliptic operators ⋮ Characterization of non-smooth pseudodifferential operators ⋮ Spectral invariance of non-smooth pseudo-differential operators ⋮ Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces ⋮ Ellipticity and invertibility in the cone algebra on \(L_p\)-Sobolev spaces ⋮ Index theory for boundary value problems via continuous fields of \(C^*\)-algebras ⋮ Remarks on 3D Boltzmann linear equation without cutoff ⋮ Spectral invariance for algebras of pseudodifferential operators on Besov-Triebel-Lizorkin spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic pseudo-differential operators - an abstract theory
• Complex powers on noncompact manifolds and manifolds with singularities
• A \(\psi ^ *\) algebra of pseudodifferential operators on noncompact manifolds
• Relative Inversion in der Störungstheorie von Operatoren und \(\Psi\)- Algebren. (Relative inversions in perturbation theory of operators and \(\Psi\)-algebras)
• Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in der \(L^ p\)-Theorie. (The spectral invariance of algebras of pseudodifferential operators in the \(L^ p\)-theory)
• A family of Fourier integral operators and the fundamental solution for a Schrödinger equation
• Weighted distribution spaces and pseudodifferential operators
• Characterization of pseudodifferential operator and application
• L\(^p\) bounds for pseudo-differential operators
• Singular Integral Equations In L p
• A Class of L p -Bounded Pseudo-Differential Operators
• A Class of Bounded Pseudo-Differential Operators

This page was built for publication: Boundedness and spectral invariance for standard pseudodifferential operators on anisotropically weighted \(L^ p\)-Sobolev spaces