Refine
Has Fulltext
- no (222) (remove)
Year of publication
Document Type
- Monograph/Edited Volume (121)
- Article (100)
- Conference Proceeding (1)
Is part of the Bibliography
- yes (222)
Keywords
- Pseudo-differential operators (3)
- Asymptotics of solutions (2)
- Edge calculus (2)
- Meromorphic operator-valued symbols (2)
- operator-valued symbols (2)
- 35J70 (1)
- 47G30 (1)
- 58J40 (1)
- Anisotropic pseudo-differential operators (1)
- Atiyah-Bott obstruction (1)
- Cone and edge pseudo-differential operators (1)
- Corner pseudo-differential operators (1)
- Edge degenerate operators (1)
- Edge symbols (1)
- Elliptic complexes (1)
- Ellipticity and parametrices (1)
- Ellipticity of corner-degenerate operators (1)
- Ellipticity of edge-degenerate operators (1)
- Fourier and Mellin transform (1)
- Fourier and Mellin transforms (1)
- Fourier transform (1)
- Fredholm property (1)
- Manifolds with boundary (1)
- Mellin (1)
- Mellin and Green operators edge symbols (1)
- Mellin operators (1)
- Mellin oscillatory integrals (1)
- Mellin quantization (1)
- Mellin quantizations (1)
- Mellin symbols with values in the edge calculus (1)
- Mellin transform (1)
- Operator-valued symbols (1)
- Operator-valued symbols of Mellin type (1)
- Operators on singular cones (1)
- Operators on singular manifolds (1)
- Pseudo-differential algebras (1)
- Quantizations (1)
- Schrodinger equation (1)
- Singular analysis (1)
- Stratified spaces (1)
- Toeplitz-type pseudodifferential operators (1)
- Twisted symbolic estimates (1)
- Volterra operator (1)
- Weighted edge spaces (1)
- Zaremba problem (1)
- algebra (1)
- asymptotic properties of eigenfunctions (1)
- boundary value problems (1)
- corner Sobolev spaces with double weights (1)
- corner parametrices (1)
- distribution with asymptotics (1)
- ellipticity (1)
- exit calculus (1)
- iterated asymptotics (1)
- manifolds with corners (1)
- manifolds with edge and boundary (1)
- many-electron systems (1)
- operator calculus (1)
- operator valued symbols (1)
- operators with corner symbols (1)
- parametrices of elliptic operators (1)
- pseudo-differential boundary value problems (1)
- pseudo-differential operators (1)
- singular manifolds (1)
- symbols (1)
- weighted Sobolev spaces (1)
- weighted edge and corner spaces (1)
We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles.
We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.