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

 

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 $J_{0}.$


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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: http://dx.doi.org/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
Published electronically: March 25, 2002
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2002 American Mathematical Society