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Theory of p-adic Distributions
Linear and Nonlinear Models

$58.00 ( ) USD

Part of London Mathematical Society Lecture Note Series

  • Date Published: December 2011
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781139119283

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About the Authors
  • This 2010 book was the first devoted to the theory of p-adic wavelets and pseudo-differential equations in the framework of distribution theory. This relatively recent theory has become increasingly important in the last decade with exciting applications in a variety of fields, including biology, image analysis, psychology, and information science. p-Adic mathematical physics also plays an important role in quantum mechanics and quantum field theory, the theory of strings, quantum gravity and cosmology, and solid state physics. The authors include many new results, some of which constitute new areas in p-adic analysis related to the theory of distributions, such as wavelet theory, the theory of pseudo-differential operators and equations, asymptotic methods, and harmonic analysis. Any researcher working with applications of p-adic analysis will find much of interest in this book. Its extended introduction and self-contained presentation also make it accessible to graduate students approaching the theory for the first time.

    • Contains introductions to the theory of p-adic numbers, p-adic functions and p-adic distributions suitable for the non-specialist
    • Contains many new results recently published in leading journals
    • Self-contained presentation makes the book suitable for use in graduate courses
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    Reviews & endorsements

    "... constitutes a relevant contribution to the study of wavelets and multiresolution analysis, as well as to the study of linear and semilinear evolution equations via wavelets, in a p-adic setting." W.A. Zuniga Galindo, Mathematical Reviews

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    Product details

    • Date Published: December 2011
    • format: Adobe eBook Reader
    • isbn: 9781139119283
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    1. p-Adic numbers
    2. p-Adic functions
    3. p-Adic integration theory
    4. p-Adic distributions
    5. Some results from p-adic L- and L- theories
    6. The theory of associated and quasi associated homogeneous p-adic distributions
    7. p-Adic Lizorkin spaces of test functions and distributions
    8. The theory of p-adic wavelets
    9. Pseudo-differential operators on the p-adic Lizorkin spaces
    10. Pseudo-differential equations
    11. p-Adic Schrödinger-type operator with point interactions
    12. Distributional asymptotics and p-adic Tauberian theorems
    13. Asymptotics of the p-adic singular Fourier integrals
    14. Nonlinear theories of p-adic generalized functions
    A. The theory of associated and quasi associated homogeneous real distributions
    B. Two identities
    C. Proof of a theorem on weak asymptotic expansions
    D. One 'natural' way to introduce a measure on Q
    References
    Index.

  • Authors

    S. Albeverio, Rheinische Friedrich-Wilhelms-Universität Bonn
    S. Albeverio is Professor in the Faculty of Mathematics and Natural Sciences at the University of Bonn, Germany.

    A. Yu Khrennikov, Växjö Universitet, Sweden
    A. Yu. Khrennikov is Professor of Applied Mathematics and Director of the International Center for Mathematical Modeling in Physics, Engineering and Cognitive Sciences at Växjö University, Sweden.

    V. M. Shelkovich, St Petersburg State University
    V. M. Shelkovich is Professor in the Mathematical Department at the St Petersburg State University of Architecture and Civil Engineering, Russia.

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