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

Authors:
Murali Rao and Li-Chien Shen

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2287-2294

MSC (2000):
Primary 31A10, 34A25

Published electronically:
March 25, 2002

MathSciNet review:
1896410

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Abstract | References | Similar Articles | Additional Information

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

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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:
https://doi.org/10.1090/S0002-9939-02-06641-8

Keywords:
Borel transform,
Bessel functions,
conjugate indicator diagram,
entire functions of exponential type,
integral equation

Received by editor(s):
December 19, 2000

Published electronically:
March 25, 2002

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2002
American Mathematical Society