Modulation Spaces

With Applications to Pseudodifferential Operators and Nonlinear Schrödinger Equations

  • Árpád Bényi
  • Kasso A. Okoudjou

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


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.


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

  • Árpád Bényi
    • 1
  • Kasso A. Okoudjou
    • 2
  1. 1.Department of MathematicsWestern Washington UniversityBellinghamUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2020
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-0716-0330-7
  • Online ISBN 978-1-0716-0332-1
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site