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

Rao, Murali; Shen, Li-Chien

doi:10.1090/S0002-9939-02-06641-8

Application of the Borel transform to the study of the spectrum of integral equations whose kernels are entire functions of exponential type
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by Murali Rao and Li-Chien Shen PDF

Proc. Amer. Math. Soc. 130 (2002), 2287-2294 Request permission

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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