Vol. 83, No. 2, 1979

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Superharmonic interpolation in subspaces of Cc(X)

Leonard Asimow

Vol. 83 (1979), No. 2, 311–323

Let E be a closed subset of the compact Hausdorff X and let A be a closed separating subspace of Cc(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
Received: 27 December 1978
Published: 1 August 1979
Leonard Asimow