Superharmonic interpolation in subspaces of C_c(X)

Leonard Asimow

Vol. 83 (1979), No. 2, 311–323

DOI: 10.2140/pjm.1979.83.311

Abstract

Let E be a closed subset of the compact Hausdorff X and let A be a closed separating subspace of C_c(X). Let ρ be a dominator (strictly positive, l.s.c.) defined on X × T, T the unit circle in C. Conditions, formulated in terms of boundary measures, are discussed for approximate and exact solutions to the problem of finding ρ-dominated extensions in A of functions g ∈ (A|_E)⁻ satisfying re tg (x) ≦ ρ(x,t) on E × T. Various interpolation theorems of Rudin-Carleson type for superharmonic dominators are incorporated into this framework.

Mathematical Subject Classification 2000

Primary: 41A05

Secondary: 46E15

Milestones

Received: 27 December 1978

Published: 1 August 1979