Orthonormal series expansion and finite spherical Hankel transform of generalized functions

Abstract

The finite spherical Hankel transformation is extended to generalized functions by using orthonormal series expansion of generalized functions. A complete orthonormal family of spherical Bessel functions is derived and certain spaces of testing functions and generalized functions are defined. The inversion and uniqueness theorems are obtained. The operational transform formula is derived and is applied to solve the problem of the propagation of heat released from a spherically symmetric point heat source.