Vol. 98, No. 2, 1982

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ISSN: 0030-8730
Operator-valued Pick’s conditions and holomorphicity

Jacob Burbea

Vol. 98 (1982), No. 2, 295–311
Abstract

The classical Pick’s conditions on disks or half-planes are extended in several directions. Specifically, these conditions are shown to be valid in any domain (or a complex manifold) in Cn, for operator-valued functions in the domain from a Hilbert space into another and for any holomorphic reproducing kernel in the domain. An interesting related result of Hindmarsh is also extended.

Mathematical Subject Classification 2000
Primary: 32A99
Secondary: 30G30, 47A99
Milestones
Received: 13 October 1980
Revised: 27 March 1981
Published: 1 February 1982
Authors
Jacob Burbea