Vol. 96, No. 1, 1981

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On some spaces of entire functions defined on infinite-dimensional spaces

J.-F. Colombeau and Mário Carvalho Matos

Vol. 96 (1981), No. 1, 63–75
Abstract

Let E be a quasi-complete dual nuclear complex locally convex space; we prove that both spaces Nb(E) and SNb(E) of entire functions of nuclear type on E introduced by Matos and Matos-Nachbin coincide with the space S(E) of the Silva holomorphic functions. As a consequence, well known results of Boland on convolution equations in (E) can be obtained as particular cases of results in Matos’s Doctoral Dissertation.

Mathematical Subject Classification 2000
Primary: 46G20
Secondary: 32A15
Milestones
Received: 14 May 1980
Revised: 16 October 1980
Published: 1 September 1981
Authors
J.-F. Colombeau
Mário Carvalho Matos