Vol. 27, No. 3, 1968

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ISSN: 0030-8730
Convolution transforms whose inversion function has complex roots in a wide angle

Zeev Ditzian

Vol. 27 (1968), No. 3, 485–496
Abstract

In this paper a class of convolution transforms:

       ∫
∞
f(x) =  −∞G (x− t)φ(t)dt
(1.1)

whose kernels G(t) satisfy

          ∫
1--  i∞      −1   st
G (t) = 2πi −i∞[E(s)]  ⋅e ds
(1.2)

where

      ∏∞                   ∏∞                  −1
E(s) =   (1− s∕ak) or E(s) =  (1− s∕ak)exp(sRea k )
k=1                  k=1
(1.3)

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

(a) For some ψ, 0 < ψ < π∕2

n=m0i,n1,2|nπ− argak| ≦ ψ where ak ⁄= 0.

(b) For some 0 < q < 1 and integer l |ak+l|q1|ak| for all k k0.

Mathematical Subject Classification
Primary: 44.25
Milestones
Received: 27 November 1967
Published: 1 December 1968
Authors
Zeev Ditzian