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＜電子ブック＞
Global Pseudo-differential Calculus on Euclidean Spaces / by Fabio Nicola, Luigi Rodino
(Pseudo-Differential Operators, Theory and Applications. ISSN:22970363 ; 4)

版	1st ed. 2010.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2010
本文言語	英語
大きさ	X, 306 p : online resource
著者標目	*Nicola, Fabio author Rodino, Luigi author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Fourier analysis LCSH:Functional analysis FREE:Differential Equations FREE:Global Analysis and Analysis on Manifolds FREE:Fourier Analysis FREE:Functional Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-7643-8512-5

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