Prolate Spheroidal Wave Functions of Order Zero, 2013
Mathematical Tools for Bandlimited Approximation

Applied Mathematical Sciences Series, Vol. 187

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Language: English

Approximative price 105.49 €

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Prolate Spheroidal Wave Functions of Order Zero
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Support: Print on demand

105.49 €

In Print (Delivery period: 15 days).

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Prolate Spheroidal Wave Functions of Order Zero
Publication date:
379 p. · 15.5x23.5 cm · Hardback

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.

​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​.- 

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.

Aimed at a broad spectrum of scientists and engineers Contains detailed description of practical numerical algorithms Written by top international researchers in field