Pseudodifferential Equations Over Non-Archimedean Spaces

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.

List of contents

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.

Report

"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)

Product details

• Authors: W. A. Zúñiga-Galindo
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 09.01.2017
• EAN: 9783319467375
• ISBN: 978-3-31-946737-5
• No. of pages: 175
• Dimensions: 181 mm x 11 mm x 235 mm
• Weight: 306 g
• Illustrations: XVI, 175 p. 1 illus.
• Series: Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Zahlentheorie, Stochastik, B, Wahrscheinlichkeitsrechnung und Statistik, Mathematische Physik, Mathematics and Statistics, Applications of Mathematics, Functional Analysis, Probability Theory and Stochastic Processes, Number Theory, Mathematical physics, Probability & statistics, Abstract Harmonic Analysis, Harmonic analysis, Probabilities, Stochastics, Probability Theory, Mathematical modelling, Mathematical Applications in the Physical Sciences, Functional analysis & transforms