The Kontorovich–Lebedev integral transformation with a Hankel function kernel in a space of generalized functions of doubly exponential descent

A version of the Kontorovich–Lebedev transformation with the Hankel function of second kind in the kernel is investigated in a space of distributions of doubly exponential descent. The inversion theorem is rigorously established making use in some steps of the proof of a relation of this transform with the Laplace one. Finally, the theory developed is illustrated in solving certain type of partial differential equations. © 2006 Elsevier Inc. All rights reserved