On a non-self adjoint eigenfunction expansion

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≤r0 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.

Keywords

• integral transforms
• eigenfunction expansion
• Bessel functions
• Hankel function.