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Pseudodifferential Equations Over Non-Archimedean Spaces

Buch | Softcover
XVI, 175 Seiten
2017 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-46737-5 (ISBN)

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Pseudodifferential Equations Over Non-Archimedean Spaces - W. A. Zúñiga-Galindo
CHF 56,90 inkl. MwSt

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.


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.

"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)

“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)

Erscheinungsdatum
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XVI, 175 p. 1 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte 11-XX • 43-XX • 46-XX • 60-XX, 70-XX • Abstract harmonic analysis • Complex analysis, complex variables • energy landscapes • Functional Analysis • Functional analysis and transforms • fundamental solutions • Igusa local zeta function • Klein-Gordon operators • Klein-Gordon operators • Markov Processes • Mathematical Applications in the Physical Sciences • Mathematical Modelling • Mathematical Physics • mathematics and statistics • Number Theory • p-adic functional analysis • parabolic-type equations • probability and statistics • Probability theory and stochastic processes • pseudodifferential operators • Schrödinger-type operators • Schrödinger-type operators • stochastics • ultrametricity
ISBN-10 3-319-46737-9 / 3319467379
ISBN-13 978-3-319-46737-5 / 9783319467375
Zustand Neuware
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