Prolate Spheroidal Wave Functions of Order Zero
Mathematical Tools for Bandlimited Approximation
Seiten
2016
|
Softcover reprint of the original 1st ed. 2013
Springer-Verlag New York Inc.
978-1-4899-7865-3 (ISBN)
Springer-Verlag New York Inc.
978-1-4899-7865-3 (ISBN)
Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.
Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool.
The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.
Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool.
The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.
Andrei Osipov is a Professor at Yale University in the Department of Mathematics.Vladimir Rokhlin is a Professor at Yale University in the Department of Computer Science. Hong Xiao is a Professor at University of California, Davis in the Department of Computer Science.
Introduction.- Mathematical and Numerical Preliminaries.- Overview.- Analysis of the Differential Operator.- Analysis of the Integral Operator.- Rational Approximations of PSWFs.-Miscellaneous Properties of PSWFs.- Asymptotic Analysis of PSWFs.- Quadrature Rules and Interpolation via PSWFs.- Numerical Algorithms.-
| Erscheinungsdatum | 04.10.2016 |
|---|---|
| Reihe/Serie | Applied Mathematical Sciences ; 187 |
| Zusatzinfo | 30 Illustrations, black and white; XI, 379 p. 30 illus. |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Technik ► Elektrotechnik / Energietechnik | |
| Schlagworte | analytical tools • Approximate Formulae for PSWF • Evaluation of the Quadrature Nodes • Intuition Behind Quadrature Weights • Numerical Algorithms • Prolate Spheroidal Wave Functions |
| ISBN-10 | 1-4899-7865-8 / 1489978658 |
| ISBN-13 | 978-1-4899-7865-3 / 9781489978653 |
| Zustand | Neuware |
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