Prolate Spheroidal Wave Functions of Order Zero [electronic resource] : Mathematical Tools for Bandlimited Approximation / by Andrei Osipov, Vladimir Rokhlin, Hong Xiao.
Contributor(s): Rokhlin, Vladimir [author.] | Xiao, Hong [author.] | SpringerLink (Online service)Material type: TextSeries: Applied Mathematical Sciences: 187Publisher: Boston, MA : Springer US : Imprint: Springer, 2013Description: XI, 379 p. 30 illus. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781461482598Subject(s): Mathematics | Numerical analysis | Applied mathematics | Engineering mathematics | Mathematics | Numerical Analysis | Signal, Image and Speech Processing | Appl.Mathematics/Computational Methods of EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 518 LOC classification: QA297-299.4Online resources: Click here to access online
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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 .- .
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.