Convolution transforms whose inversion function has complex roots in a wide angle

Zeev Ditzian

Vol. 27 (1968), No. 3, 485–496

DOI: 10.2140/pjm.1968.27.485

Abstract

In this paper a class of convolution transforms:

(1.1)

whose kernels G(t) satisfy

(1.2)

where

(1.3)

will be treated. Investigation of properties will be carried for the subclass defined by the restriction on a_k as follows:

(a) For some ψ, 0 < ψ < π∕2

(b) For some 0 < q < 1 and integer l |a_k+l|≧ q⁻¹|a_k| for all k ≧ k₀.

Mathematical Subject Classification

Primary: 44.25

Milestones

Received: 27 November 1967

Published: 1 December 1968