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

DOI: 10.2140/pjm.1981.96.63

Abstract

Let E be a quasi-complete dual nuclear complex locally convex space; we prove that both spaces ℋ_N^b(E) and ℋ_SN^b(E) of entire functions of nuclear type on E introduced by Matos and Matos-Nachbin coincide with the space ℋ_S(E) of the Silva holomorphic functions. As a consequence, well known results of Boland on convolution equations in ℋ(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