Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the eigenfunctions corresponding to the bandpass kernel, in the case of degeneracy


Author: J. A. Morrison
Journal: Quart. Appl. Math. 21 (1963), 13-19
MSC: Primary 45.12
DOI: https://doi.org/10.1090/qam/145306
MathSciNet review: 145306
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Abstract: It has previously been pointed out that the eigenfunctions of the finite integral equation with bandlimited difference kernel satisfy a certain second order linear differential equation, containing one parameter, whose continuous solutions, for discrete values of the parameter, are the prolate spheroidal wave functions. We consider here the finite integral equation with bandpass difference kernel. It is shown that, in the case of degeneracy, one eigenfunction is the continuous solution of a certain fourth order linear differential equation, containing two parameters which must be determined from prescribed conditions. The second eigenfunction is the derivative of the first one.


References [Enhancements On Off] (What's this?)

  • [1] D. Slepian, Estimation of signal parameters in the presence of noise, IRE Trans. Infor. Theory, PGIT-3, (1954) 68-89
  • [2] D. Slepian, private communication
  • [3] D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty. I, Bell System Tech. J. 40 (1961), 43–63. MR 0140732, https://doi.org/10.1002/j.1538-7305.1961.tb03976.x
  • [4] J. A. Morrison, On the commutation of finite integral operators, with difference kernels, and linear self-adjoint differential operators.
  • [5] Carson Flammer, Spheroidal wave functions, Stanford University Press, Stanford, California, 1957. MR 0089520

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DOI: https://doi.org/10.1090/qam/145306
Article copyright: © Copyright 1963 American Mathematical Society


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