Vol. 106, No. 1, 1983

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H∞-interpolation from a subset of the boundary

Frank Hayne Beatrous, Jr.

Vol. 106 (1983), No. 1, 23–31
Abstract

We obtain necessary and sufficient conditions for a bounded function on an open subset of the boundary of a smooth, bounded domain D in Cn to be the restriction of a holomorphic function from D into the unit disc. Our condition is a quadratic inequality involving the Szegő kernel of D which is the boundary analogue of the classical Pick-Nevanlinna condition for interpolation in the unit disc.

Mathematical Subject Classification 2000
Primary: 32A35
Secondary: 47B35
Milestones
Received: 15 September 1981
Published: 1 May 1983
Authors
Frank Hayne Beatrous, Jr.