Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions

Applied and Computational Harmonic Analysis

Volumn 15, Issue 2, 2003, Pages 168-176

  Boyd, John P ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; FUNCTION EVALUATION; GEOMETRY; INTEGRAL EQUATIONS;

BANDLIMITED FUNCTION; PROLATE SPHEROIDAL FUNCTIONS;

APPROXIMATION THEORY;

EID: 0347480334     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1063-5203(03)00048-4     Document Type: Letter

References (7)

1. J.P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd Edition, Dover, New York, 2001, p. 665.
2. J.P. Boyd, A comparison of numerical algorithms for Fourier Extension of the First, Second and Third Kinds, J. Comput. Phys. 178 (2002) 118-160.
3. J.P. Boyd, Asymptotic Fourier coefficients for a C∞ bell (Smoothed-"Top-Hat" Function) and the Fourier Extension problem, Appl. Comput. Harmon. Anal. (2003), submitted for publication.
4. J.P. Boyd, Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral and pseudospectral algorithms, J. Comput. Phys. (2003), submitted for publication.
5. D. Slepian, Some comments on Fourier analysis, uncertainty and modeling, SIAM Rev. (1983) 379-393.
6. H. Xiao, V. Rokhlin, N. Yarvin, Prolate spheroidal wavefunctions, quadrature and interpolation, Inverse Problems 17 (2001) 805-838.
7. A.I. Zayed, Handbook of Function and Generalized Function Transformations, in: Mathematical Sciences Reference Series, Vol. 3, CRC Press, Boca Raton, FL, 1996.