An operational calculus for a Mehler-Fock type index transform on distributions of compact support

In this paper, we present a systematic analysis of an operational calculus which is based upon a Mehler-Fock type index transform on distributions of compact support over the interval (1,8). By means of this transform, we obtain a distribution f on the interval (1,8), which satisfies an equation of the type P (A(t)')u = g, where P denotes any polynomial with no zeros in the interval (-infinity,- 1/4], A(t)(') represents the adjoint of the differential operator At = Dt (t2 - 1) Dt, the distribution g has compact support on (1,infinity) and u is an unknown distribution on (1,infinity).

Automated summary

In this paper, we analyze an operational calculus based on the Mehler-Fock type index transform on distributions of compact support over the interval (1,8). Using this transform, we obtain a distribution f on the interval (1,8) that satisfies an equation of the form P (A(t)')u = g, where P is any polynomial with no zeros in the interval (-infinity,- 1/4], A(t)(') is the adjoint of the differential operator At = Dt (t2 - 1) Dt, the distribution g has compact support on (1,infinity), and u is an unknown distribution on (1,infinity).