Pseudodifferential Equations Over Non-Arch...

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Beschreibung

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 mainlywith the theory and applications of p-adic wavelets.

Zusammenfassung

Offers a fast introduction to the theory of pseudodifferential equations over non-Archimedean fields and their connections with mathematical physics, probability and number theory

Provides a very general theory of parabolic-type equations and their Markov processes motivated by the models of hierarchic complex systems introduced by Avetisov et al. in around 2000

Combines methods of PDEs, probability and number theory

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Medium:	Taschenbuch
Seiten:	196
Reihe:	Lecture Notes in Mathematics
Inhalt:	xvi 175 S. 1 s/w Illustr. 175 p. 1 illus.
ISBN-13:	9783319467375
ISBN-10:	3319467379
Sprache:	Englisch
Herstellernummer:	978-3-319-46737-5
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Zúñiga-Galindo, W. A.
Auflage:	1st ed. 2016
Hersteller:	Springer International Publishing Lecture Notes in Mathematics
Maße:	235 x 155 x 11 mm
Von/Mit:	W. A. Zúñiga-Galindo
Erscheinungsdatum:	09.01.2017
Gewicht:	0,306 kg

preigu-id: 108191829