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Local ideals in a
topological algebra of entire functions characterized by a
non-radial rate of growth
James Jerome Metzger |
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Vol. 51 (1974), No. 1, 251–256
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Abstract |
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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(∥x∥ρ + ∥y∥σ)]} 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
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Milestones
Received: 14 November 1972
Revised: 20 July 1973
Published: 1 March 1974
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Authors |
| James Jerome Metzger | |
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