Global Pseudo-Differential Calculus on Euclidean Spaces [electronic resource] /by Fabio Nicola, Luigi Rodino.
by Nicola, Fabio [author.]; Rodino, Luigi [author.]; SpringerLink (Online service).
Material type:
BookSeries: Pseudo-Differential Operators, Theory and Applications: 4Publisher: Basel : Birkhäuser Basel, 2010.Description: X, 306 p. online resource.ISBN: 9783764385125.Subject(s): Mathematics | Fourier analysis | Functional analysis | Global analysis | Differential equations, partial | Mathematics | Partial Differential Equations | Global Analysis and Analysis on Manifolds | Fourier Analysis | Functional AnalysisDDC classification: 515.353 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA370-380 (Browse shelf) | Available |
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| QA8.9-10.3 Kripke’s Worlds | QA639.5-640.7 q-Clan Geometries in Characteristic 2 | QA299.6-433 Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators | QA370-380 Global Pseudo-Differential Calculus on Euclidean Spaces | QA370-380 Pseudo-Differential Operators and Symmetries | QA8.9-10.3 Completeness Theory for Propositional Logics | Quantum Spaces |
Background meterial -- Global Pseudo-Differential Calculus -- ?-Pseudo-Differential Operators and H-Polynomials -- G-Pseudo-Differential Operators -- Spectral Theory -- Non-Commutative Residue and Dixmier Trace -- Exponential Decay and Holomorphic Extension of Solutions.
This book is devoted to the global pseudo-differential calculus on Euclidean spaces and its applications to geometry and mathematical physics, with emphasis on operators of linear and non-linear quantum physics and travelling waves equations. The pseudo-differential calculus presented here has an elementary character, being addressed to a large audience of scientists. It includes the standard classes with global homogeneous structures, the so-called G and gamma operators. Concerning results for the applications, a first main line is represented by spectral theory. Beside complex powers of operators and asymptotics for the counting function, particular attention is here devoted to the non-commutative residue in Euclidean spaces and the Dixmier trace. Second main line is the self-contained presentation, for the first time in a text-book form, of the problem of the holomorphic extension of the solutions of the semi-linear globally elliptic equations. Entire extensions are discussed in detail. Exponential decay is simultaneously studied.
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