Interpolating sequences for functions satisfying a Lipschitz condition

Eric P. Kronstadt

Vol. 63 (1976), No. 1, 169–177

DOI: 10.2140/pjm.1976.63.169

Abstract

Let D be the unit disk in C, Lip (D) the space of functions, f, holomorphic in D, continuous on D and satisfying a Lipschitz condition:

If S = {a_i}_x=1^∞∈ D is a discrete sequence with no accumulation points in D, let Lip (S) be the set of functions, g, defined on S satisfying

We say S is a Lip (D) interpolating (LI) sequence if the restriction mapping from Lip (D) to Lip (S) given by f → f|S is surjective. Our aim is to describe some of the properties of such sequences and to give some examples. Specifically we show that an LI sequence must either be a uniformly separated sequence, or the union of two such sequences which approach one another as they tend to ∂D.

Mathematical Subject Classification

Primary: 30A80, 30A80

Milestones

Received: 4 November 1974

Published: 1 March 1976