On a class of convolution transforms

Zeev Ditzian

Vol. 25 (1968), No. 1, 83–107

DOI: 10.2140/pjm.1968.25.83

Abstract

In this paper the convolutian transform

(1.1)

whose kernel G(t) is the Fourier transform of [E(iy)]⁻¹ where E(s) is defined by

will be studied. An inversion theory similar to that achieved when a_k of (1.2) are real will be obtained. The results will show that under certain rather weak conditions, an infinite subsequence a_k(i) of a_k can satisfy

Classes of transforms will be introduced that allow the occurrence of min{|arg a_k|,|arg −a_k|}≧ π∕4 for all k.

Mathematical Subject Classification

Primary: 44.25

Milestones

Received: 20 December 1966

Published: 1 April 1968