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© 2020

Modulation Spaces

With Applications to Pseudodifferential Operators and Nonlinear Schrödinger Equations

Book

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Árpád Bényi, Kasso A. Okoudjou
    Pages 1-33
  3. Árpád Bényi, Kasso A. Okoudjou
    Pages 35-59
  4. Árpád Bényi, Kasso A. Okoudjou
    Pages 61-76
  5. Árpád Bényi, Kasso A. Okoudjou
    Pages 77-106
  6. Árpád Bényi, Kasso A. Okoudjou
    Pages 107-117
  7. Árpád Bényi, Kasso A. Okoudjou
    Pages 119-126
  8. Árpád Bényi, Kasso A. Okoudjou
    Pages 127-140
  9. Back Matter
    Pages 141-169

About this book

Introduction

This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource.

Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers.

Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.

Keywords

Modulation spaces Time–frequency analysis Nonlinear modulation spaces Functional analysis Harmonic analysis Real analysis Unweighted modulation spaces Nonlinear Schrödinger Equations Pseudodifferential operators Nonlinear partial differential equations Foundations of time-frequency analysis Partial differential equations Besov spaces Gabor frames Triebel–Lizorkin spaces

Authors and affiliations

  1. 1.Department of MathematicsWestern Washington UniversityBellinghamUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

Bibliographic information

  • Book Title Modulation Spaces
  • Book Subtitle With Applications to Pseudodifferential Operators and Nonlinear Schrödinger Equations
  • Authors Árpád Bényi
    Kasso A. Okoudjou
  • Series Title Applied and Numerical Harmonic Analysis
  • Series Abbreviated Title Applied,Numerical Harmonic Analysis
  • DOI https://doi.org/10.1007/978-1-0716-0332-1
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2020
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-0716-0330-7
  • Softcover ISBN 978-1-0716-0614-8
  • eBook ISBN 978-1-0716-0332-1
  • Series ISSN 2296-5009
  • Series E-ISSN 2296-5017
  • Edition Number 1
  • Number of Pages XVI, 169
  • Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
  • Topics Fourier Analysis
    Operator Theory
    Partial Differential Equations
    Functional Analysis
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