Abstract
We consider the operator M of convolving a function g supported in the finite interval [-1,1] with the Hankel function . We derive a characterization of the range of M, considered as an operator on LP ([—1,1]), in terms of the Hilbert transform. This characterization can be used as a starting point for solving the integral equation Mg=f with f contained in the range of M. The characterization of the range of M is obtained by applying contour integration methods in the complex plane and it can be expected that by applying such techniques also the ranges of other integral operators can be characterized
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