Vol. 37, No. 2, 1971

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The functions of bounded index as a subspace of a space of entire functions

Keith A. Ekblaw

Vol. 37 (1971), No. 2, 353–355
Abstract

Let f(z) = n=0anzn and g(z) = n=0bnzn be entire functions. Define d(f,g) = Sup{|a0b0|,(|anbrν|)1∕nn = 1,2,}. It is the purpose of this note to show that, in the topology generated by d, the entire functions of bounded index, B, are of the first category.

Mathematical Subject Classification
Primary: 30A98
Milestones
Received: 19 October 1970
Revised: 11 January 1971
Published: 1 May 1971
Authors
Keith A. Ekblaw