Global Pseudo-Differential Calculus on Euclidean Spaces

• Κύριοι συγγραφείς: Nicola, Fabio (Συγγραφέας), Rodino, Luigi (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2010.
• Σειρά: Pseudo-Differential Operators, Theory and Applications ; 4
• Θέματα: Mathematics.; Fourier analysis.; Functional analysis.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Partial Differential Equations.; Global Analysis and Analysis on Manifolds.; Fourier Analysis.; Functional Analysis.

 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. 

 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.