Refine
Year of publication
Document Type
- Monograph/Edited Volume (121)
- Article (101)
- Conference Proceeding (1)
- Postprint (1)
- Preprint (1)
Is part of the Bibliography
- yes (225) (remove)
Keywords
- Pseudo-differential operators (4)
- Asymptotics of solutions (2)
- Edge calculus (2)
- Mellin symbols with values in the 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)
- Boutet de Monvel's calculus (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)
- Kegel space (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 transform (1)
- Operator-valued symbols (1)
- Operator-valued symbols of Mellin type (1)
- Operators on manifolds with second order singularities (1)
- Operators on singular cones (1)
- Operators on singular manifolds (1)
- Parametrices of elliptic operators (1)
- Pseudo-differential algebras (1)
- Quantizations (1)
- Schrodinger equation (1)
- Singular analysis (1)
- Singular cones (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)
- continuity in Sobolev spaces with double weights (1)
- corner Sobolev spaces with double weights (1)
- corner parametrices (1)
- distribution with asymptotics (1)
- edge quantizations (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 establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.
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.