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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
MathSciNet review:
1896410
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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 
References:
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- 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.
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- 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
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Additional Information:
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
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