International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 235-248
On a non-self adjoint eigenfunction expansion
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 , in which varies over a truncated infinite interval , where and the parameter is complex. This kind of transform is useful in the investigation of functions that satisfy the Helmholtz equation and the condition of radiation.