Vol. 51, No. 1, 1974

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Local ideals in a topological algebra of entire functions characterized by a non-radial rate of growth

James Jerome Metzger

Vol. 51 (1974), No. 1, 251–256
Abstract

In this paper a class of locally convex algebras of entire functions is considered: For fixed ρ > 0,σ > 0, and n a positive integer, let E[ρ,σ;n] denote the space of all entire functions f in n variables which satisfy |f(x + iy)| = 0{exp[A(xρ + yσ)]} for some A > 0. Sufficient conditions are given in order that the local ideal generated by a family in E[ρ,σ;n] coincides with the closed ideal generated by the family.

Mathematical Subject Classification 2000
Primary: 46E25
Secondary: 32A15
Milestones
Received: 14 November 1972
Revised: 20 July 1973
Published: 1 March 1974
Authors
James Jerome Metzger