Proceedings of the American Mathematical Society

Application of the Borel transform to the study of the spectrum of integral equations whose kernels are entire functions of exponential type

Author(s): Murali Rao; Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 130 (2002), 2287-2294.
MSC (2000): Primary 31A10, 34A25
Posted: March 25, 2002
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract: Using the Borel transform, we study the spectrum of a class of non-compact integral operators whose kernels are of exponential type and square integrable on the real line. Our method also enables us to obtain an interesting characterization of a well-known integral equation involving the Bessel function $J_{0}.$

1.: H. Dym and H.P. McKean, Fourier Series and Integral, Academic Press, New York, 1972. MR 56:945
2.: W.H.J. Fuchs, On the eigenvalues of an integral equation arising in the theory of band limited signals, J. Math. Anal. Appl. 9(1964), 317-330. MR 30:4128
3.: B. Ja. Levin, Distribution of Zeros of Entire Functions, Amer. Math. Soc., Providence, R.I., 1964. MR 28:217; Russian transl. MR 81k:30011
4.: H.O. Pollack and D. Slepian, Prolate spheroidal wave functions Fourier analysis and uncertainty (1), Bell System Tech. J. 40(1961), 43-64.
5.: W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. MR 35:1420
6.: G.N. Watson, A Treatise on the Theory of Bessel Functions, second edition, Cambridge University Press, London 1962. MR 6:64a; reprint MR 96i:33010

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 31A10, 34A25

Murali Rao
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: rao@math.ufl.edu

Li-Chien Shen
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: shen@math.ufl.edu

DOI: 10.1090/S0002-9939-02-06641-8
PII: S 0002-9939(02)06641-8
Keywords: Borel transform, Bessel functions, conjugate indicator diagram, entire functions of exponential type, integral equation
Received by editor(s): December 19, 2000
Posted: March 25, 2002
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2002, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS