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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Authors: Frank Beatrous and Jacob Burbea
Journal: Trans. Amer. Math. Soc. 284 (1984), 247-270
MSC: Primary 32E30; Secondary 30C40, 46E20
DOI: https://doi.org/10.1090/S0002-9947-1984-0742424-4
MathSciNet review: 742424
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0742424-4
Keywords: Positive-definiteness, functional Hilbert spaces, holomorphic interpolation
Article copyright: © Copyright 1984 American Mathematical Society