Modulation Spaces : With Applications to Pseudodifferential Operators and Nonlinear Schrödinger Equations. 1st ed. 2020

種類:

電子ブック

責任表示:

by Árpád Bényi, Kasso A. Okoudjou

出版情報:

New York, NY : Springer New York : Imprint: Birkhäuser, 2020

著者名:

• Bényi, Árpád.
• Okoudjou, Kasso A.
• SpringerLink (Online service)

シリーズ名:

Applied and Numerical Harmonic Analysis ;

ISBN:

9781071603321 [1071603329]    

注記:

Notions of real, functional and Fourier analysis -- Modulation spaces -- Equivalent definitions of modulation spaces -- Pseudodifferential operators -- Weighted modulation spaces -- Modulation spaces and other function spaces -- Applications to partial differential equations -- A proof of Banach's fixed point theorem -- The Picard-Lindelöf and Peano theorems -- Gronwall's lemma -- Local well-posedness of NLS on Sobolev spaces.
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-fre

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