Vol. 15, No. 3, 1965

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Topologies for Laplace transform spaces

Donald Earl Myers

Vol. 15 (1965), No. 3, 957–960

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
Received: 24 April 1964
Published: 1 September 1965
Donald Earl Myers