International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 235-248
doi:10.1155/S0161171284000247
On a non-self adjoint eigenfunction expansion
D. Naylor
Department of Applied Mathematics, The University of Western Ontario, Ontario, London N6A 5B9, Canada
Abstract
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 a≤r<∞, 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.