Vol. 31, No. 3, 1969

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Subspace kernels and minimum problems in Hilbert spaces with kernel function

Bruce Langworthy Chalmers

Vol. 31 (1969), No. 3, 619–628
Abstract

The purpose of this paper is to extend the theory of Hilbert spaces with kernel function to obtain first the kernel function of any subspace described as the intersection of the nullspaces of countably many continuous linear functionals, and secondly the solution of minimum norm to interpolation problems involving countably many linear side conditions. The results are then applied to obtain in §1 a class of pseudoconformally invariant functions in Cn and in §2 further results on the classical interpolation problem involving pointwise evaluation.

Mathematical Subject Classification 2000
Primary: 46E15
Secondary: 32H10, 30A80
Milestones
Received: 3 April 1969
Published: 1 December 1969
Authors
Bruce Langworthy Chalmers