Topologies for Laplace transform spaces

Donald Earl Myers

Vol. 15 (1965), No. 3, 957–960

DOI: 10.2140/pjm.1965.15.957

Abstract

In this paper four topologies are compared:

(i) an L₂-type topology on the space of functions having bilateral transforms,

(ii) an L₁ and (iii) an L₂-type topology on the space of transforms, and

(iv) finally that of one form of convergence of compact subsets for the space of analytic functions. It is shown that sequential convergence in (i) implies (iii) and (iv) and (ii) implies (i) and (iv) and hence (iii).

Mathematical Subject Classification

Primary: 44.10

Milestones

Received: 24 April 1964

Published: 1 September 1965