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

Keith A. Ekblaw

Vol. 37 (1971), No. 2, 353–355

DOI: 10.2140/pjm.1971.37.353

Abstract

Let f(z) = ∑ _n=0^∞a_nzⁿ and g(z) = ∑ _n=0^∞b_nzⁿ be entire functions. Define d(f,g) = Sup{|a₀−b₀|,(|a_n−b_rν|)^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