Pseudodifferential Equations Over Non-Archimedean Spaces

AvW. A. Zúñiga-Galindo

Häftad, Engelska, 2017

Del 2174 i serien Lecture Notes in Mathematics

425 kr

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526 kr

Beskrivning

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.

Produktinformation

Utgivningsdatum:2017-01-09
Mått:155 x 235 x 11 mm
Vikt:306 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:175
Upplaga:17001
Förlag:Springer International Publishing AG
ISBN:9783319467375

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Recensioner i media

“The book is a valuable contribution to the literature on non-Archimedean analysis and mathematical physics. It will be useful for both specialists and students studying this subject.” (Anatoly N. Kochubei, Mathematical Reviews, October, 2017)

Innehållsförteckning

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.

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