Positive-definiteness and its applications to interpolation problems for holomorphic functions

Beatrous, Frank; Burbea, Jacob

doi:10.1090/S0002-9947-1984-0742424-4

Positive-definiteness and its applications to interpolation problems for holomorphic functions
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by Frank Beatrous and Jacob Burbea

Trans. Amer. Math. Soc. 284 (1984), 247-270

DOI: https://doi.org/10.1090/S0002-9947-1984-0742424-4

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Abstract:

Holomorphic interpolation problems of the Pick-Nevanlinna and Loewner types as well as abstract interpolation theorems on functional Hilbert spaces are considered. Various characterizations are presented for restrictions of bounded holomorphic functions. In addition, certain norm estimates for restrictions and extensions of holomorphic functions are obtained.

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