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A spectral approach to an integral equation

Published online by Cambridge University Press:  18 May 2009

W. Lamb
W. Lamb
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
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In a recent paper [7], Rooney used a technique involving the Mellin transform to obtain solutions in certain spaces ℒμ, ρ of an integral equation which had been studied previously by Šub-Sizonenko [9]. The integral equation in question can be written as

where I denotes the identity operator and G0.1/2 is given by

with the inversion formula obtained by Rooney taking the form

Rooney verified that (1.1) and (1.2) formed an inversion pair in ℒμ, ρ for 1 ≤ p < ∞ and μ > 0.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 83 - 89
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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