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Fourier Series, Fourier Transform and Their Applications to Mathematical Physics

  • Valery Serov

Part of the Applied Mathematical Sciences book series (AMS, volume 197)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Fourier Series and the Discrete Fourier Transform

  3. Fourier Transform and Distributions

    1. Front Matter
      Pages 129-129
    2. Valery Serov
      Pages 131-132
    3. Valery Serov
      Pages 133-141
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      Pages 153-165
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      Pages 167-173
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      Pages 175-192
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      Pages 193-205
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      Pages 217-244
  4. Operator Theory and Integral Equations

    1. Front Matter
      Pages 245-245
    2. Valery Serov
      Pages 247-248
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      Pages 249-259
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      Pages 261-278
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      Pages 279-293
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      Pages 295-311
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      Pages 313-317
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      Pages 319-330
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      Pages 331-334
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      Pages 335-347
    11. Valery Serov
      Pages 349-358
    12. Valery Serov
      Pages 371-378
    13. Valery Serov
      Pages 379-389
  5. Partial Differential Equations

    1. Front Matter
      Pages 391-391
    2. Valery Serov
      Pages 393-403
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      Pages 405-419
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      Pages 421-435
    5. Valery Serov
      Pages 437-449
    6. Valery Serov
      Pages 451-469
    7. Valery Serov
      Pages 471-483
    8. Valery Serov
      Pages 507-516

About this book

Introduction

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts.

The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations.

Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering. 

Keywords

Fourier Series Fourier Transforms Operator Theory Mathematical Phsycis Partial Differential Equations Freidrich's Extension Schrodinger Operator Scattering Theory Sobolev Spaces Born Approximation Elliptic Operator Fundamental Solution Reisz Theory

Authors and affiliations

  • Valery Serov
    • 1
  1. 1.Department of Mathematical SciencesUniversity of OuluOuluFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-65262-7
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-65261-0
  • Online ISBN 978-3-319-65262-7
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site