Operator-valued Pick’s conditions and holomorphicity

Jacob Burbea

Vol. 98 (1982), No. 2, 295–311

DOI: 10.2140/pjm.1982.98.295

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