Complex inversion for the generalized convolution transformation

J. N. Pandey and Armen H. Zemanian

Vol. 25 (1968), No. 1, 147–157

DOI: 10.2140/pjm.1968.25.147

Abstract

The complex inversion theory for the convolution transformation, which is due to Hirschman and Widder, is extended to certain generalized functions. This is accomplished by transferring the complex inversion formula onto the testing function space for the generalized function under consideration and then showing that the limiting process in the resulting formula converges with respect to the topology of the testing function space.

Mathematical Subject Classification

Primary: 44.25

Secondary: 46.00

Milestones

Received: 20 December 1966

Published: 1 April 1968