Prolate Spheroidal Wave Functions of Order Zero

Mathematical Tools for Bandlimited Approximation
2013
ISBN: 978-1-4614-8258-1
Verlag: Springer US

Buch, Englisch, Band 187, 379 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 7096 g

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Osipov, Andrei

Xiao, Hong

Rokhlin, Vladimir

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

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.-

Über Autor(innen)

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.