Vol. 24, No. 2, 1968

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ISSN: 0030-8730
A note on functions which operate

Alan G. Konheim and Benjamin Weiss

Vol. 24 (1968), No. 2, 297–302
Abstract

Let A,denote two families of functions a,b : X Y. A function F : Z Y Y is said to operate in (A,) provided that for each a A with range (a) Z we have F(a) ∈ℬ. Let G denote a locally compact Abelian group. In this paper we characterize the functions which operate in two cases:

  1. A = Φr(G) = positive definite functions on G with ϕ(e) = r and = Oi.d.,s(G) = infinitely divisible positive definite functions on G with ϕ(e) = s.
  2. A = = Φ1(G) = Log Φi.d.,1(G).

Mathematical Subject Classification
Primary: 42.54
Milestones
Received: 12 July 1966
Published: 1 February 1968
Authors
Alan G. Konheim
Benjamin Weiss