Prolate Spheroidal Wave Functions of Order Zero: Mathematical Tools for Bandlimited Approximation

ISBN-13: 9781489978653 / Angielski / Miękka / 2016 / 379 str.

Andrei Osipov; Vladimir Rokhlin; Hong Xiao

Opis

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.

Spis treści

​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​.- 

O autorze

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.

Blurb

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 PSWF as an analytical tool to electrical engineers designing filters and antennas.