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＜電子ブック＞
Pseudodifferential Equations Over Non-Archimedean Spaces / by W. A. Zúñiga-Galindo
(Lecture Notes in Mathematics. ISSN:16179692 ; 2174)

版	1st ed. 2016.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2016
本文言語	英語
大きさ	XVI, 175 p. 1 illus : online resource
著者標目	*Zúñiga-Galindo, W. A author SpringerLink (Online service)
件　名	LCSH:Harmonic analysis LCSH:Functional analysis LCSH:Mathematical physics LCSH:Number theory LCSH:Probabilities FREE:Abstract Harmonic Analysis FREE:Functional Analysis FREE:Mathematical Physics FREE:Number Theory FREE:Probability Theory
一般注記	p-Adic Analysis: Essential Ideas and Results -- Parabolic-type Equations and Markov Processes -- Non-Archimedean Parabolic-type Equations With Variable Coefficients -- Parabolic-Type Equations on Adeles -- Fundamental Solutions and Schrödinger Equations -- Pseudodifferential Equations of Klein-Gordon Type Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applications of p-adic wavelets HTTP:URL=https://doi.org/10.1007/978-3-319-46738-2

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