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Online ISSN 1552-4485; Print ISSN 0033-569X
Eigenfunctions corresponding to the band pass kernel with large center frequency
Author:
A. J. Jerri
Journal:
Quart. Appl. Math. 27 (1970), 523-525
DOI:
https://doi.org/10.1090/qam/99808
MathSciNet review:
QAM99808
Full-text PDF Free Access
Abstract | References | Additional Information
Abstract: It is known that the eigenfunctions of the finite integral equation with band limited difference kernel are the prolate spheroidal wave functions. When the band pass difference kernel was considered, no such well-known functions were found, except for the limiting case of zero band width. In this report we show that for large values of the center frequency the eigenfunctions corresponding to the band pass kernel are related to the prolate spheroidal functions.
- D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty. I, Bell System Tech. J. 40 (1961), 43–63. MR 140732, DOI https://doi.org/10.1002/j.1538-7305.1961.tb03976.x
- J. A. Morrison, On the eigenfunctions corresponding to the bandpass kernel, in the case of degeneracy, Quart. Appl. Math. 21 (1963), 13–19. MR 145306, DOI https://doi.org/10.1090/S0033-569X-1963-0145306-9 W. M. Stone and R. L. Brock, On the probability of detection with a post detection filter, Boeing D-16921, Seattle (1955)
- Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
- Philip Franklin, A Treatise on Advanced Calculus, John Wiley & Sons, Inc., New York, 1940. MR 0002571
- David Slepian, Some asymptotic expansions for prolate spheroidal wave functions, J. Math. and Phys. 44 (1965), 99–140. MR 179392
Additional Information
Article copyright:
© Copyright 1970
American Mathematical Society