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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on the representation of zero by solutions of differential equations


Authors: Jet Wimp and David Colton
Journal: Proc. Amer. Math. Soc. 74 (1979), 232-234
MSC: Primary 34B25; Secondary 33A40
MathSciNet review: 524292
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Abstract: Numerical evidence from certain problems arising in optics seems to indicate Fourier-Bessel series which converge to zero in $ (1 - \delta ,1]$ also converge to zero in $ [1,1 + \delta )$, an interval which lies outside the range of orthogonality of the Bessel functions. Here we demonstrate this as a corollary of a result on series of functions which satisfy a general Sturm-Liouville equation.


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

  • [1] B. Ja. Levin, Distribution of zeros of entire functions, American Mathematical Society, Providence, R.I., 1964. MR 0156975 (28 #217)
  • [2] P. Wiersma, The realization of circularly symmetric positive filter functions by transparent rings, Technical Report, Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands, 1978.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524292-2
PII: S 0002-9939(1979)0524292-2
Keywords: Fourier-Bessel series, uniqueness sets, representations of zero, orthogonal functions
Article copyright: © Copyright 1979 American Mathematical Society