Published by Springer, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer International Publishing Jan 2017, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 196 pp. Englisch.
Published by Springer 2017-01, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer International Publishing, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.
Published by Springer, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer Verlag, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
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Published by Springer, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Published by Springer International Publishing, 2017
ISBN 10: 3319467379 ISBN 13: 9783319467375
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 gen.
Published by Springer, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
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Published by Cambridge University Press, 2018
ISBN 10: 1107188822 ISBN 13: 9781107188822
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ISBN 10: 1107188822 ISBN 13: 9781107188822
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Published by Springer, 2021
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Published by Springer, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
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Published by Cambridge University Press, 2018
ISBN 10: 1107188822 ISBN 13: 9781107188822
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Published by Springer, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
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Published by Cambridge University Press, 2018
ISBN 10: 1107188822 ISBN 13: 9781107188822
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Published by Springer, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
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Published by Springer, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
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Published by Springer, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
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Published by Cambridge Univ Pr, 2018
ISBN 10: 1107188822 ISBN 13: 9781107188822
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Published by Springer International Publishing Dez 2021, 2021
ISBN 10: 3030819752 ISBN 13: 9783030819750
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology.In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role - a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems - for instance,proteins - asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more.This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences. 336 pp. Englisch.