Abstract
Let L⋆ be a filtered algebra of abstract pseudodifferential operators equipped with a notion of ellipticity, and T⋆ be a subalgebra of operators of the form P1AP0, where P0,P1∈L⋆ are projections, i.e., Pj2=Pj. The elements of L⋆ act as linear continuous operators in a scale of abstract Sobolev spaces, those of T⋆ in the corresponding subspaces determined by the projections. We study how the ellipticity in L⋆ descends to T⋆, focusing on parametrix construction, equivalence with the Fredholm property, characterisation in terms of invertibility of principal symbols, and spectral invariance. Applications concern SG-pseudodifferential operators, operators on manifolds with conical singularities, and Boutet de Monvelʼs algebra for boundary value problems. In particular, we derive invertibility of the Stokes operator with Dirichlet boundary conditions in a subalgebra of Boutet de Monvelʼs algebra. We indicate how the concept generalizes to parameter-dependent operators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Electroencephalography and Clinical Neurophysiology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
