Vol. 100, No. 1, 1982

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Interpolation, continuation, and quadratic inequalities

Walter Hengartner and Glenn E. Schober

Vol. 100 (1982), No. 1, 139–151

1. C. H. FitzGerald considered conditions for interpolating the values of an analytic function in terms of quadratic inequalities. In addition, he used them to obtain an interesting result concerning analytic continuation of functions of two variables and related them to Pick-Nevanlinna interpolation.

We shall show that these theorems follow directly from well-known principles of functional analysis. Since these principles are not limited to interpolating values of an analytic function, we shall obtain applications to interpolating functional values of both analytic and harmonic functions of several variables. In addition, we obtain analogous applications to analytic and harmonic continuation and to Pick-Nevanlinna interpolation.

Mathematical Subject Classification 2000
Primary: 32H10
Secondary: 30E05
Received: 3 November 1980
Revised: 29 December 1980
Published: 1 May 1982
Walter Hengartner
Glenn E. Schober