International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 235-248

On a non-self adjoint eigenfunction expansion

D. Naylor

Department of Applied Mathematics, The University of Western Ontario, Ontario, London N6A 5B9, Canada

Received 6 June 1983

Copyright © 1984 D. Naylor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops a formula of inversion for an integral transform similar to that associated with the names of Kontorovich and Lebedev. The kernel involves the Hankel function Hu(1)(kr), in which r varies over a truncated infinite interval ar<, where a>0 and the parameter k is complex. This kind of transform is useful in the investigation of functions that satisfy the Helmholtz equation and the condition of radiation.