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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Minimal $ H\sp{2}$ interpolation in the Carathéodory class


Authors: E. Beller and B. Pinchuk
Journal: Proc. Amer. Math. Soc. 72 (1978), 289-293
MSC: Primary 30D50
DOI: https://doi.org/10.1090/S0002-9939-1978-0507325-8
MathSciNet review: 507325
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Abstract: For $ ({c_1}, \ldots ,{c_n})$ in $ {{\mathbf{C}}^n}$, let $ C({c_1}, \ldots ,{c_n})$ denote the class of functions $ f(z) = 1 + {c_1}z + \cdots + {c_n}{z^n} + \Sigma _{k = n + 1}^\infty {a_k}{z^k}$ which are analytic and satisfy $ \operatorname{Re} f(z) > 0$ in the unit disc. The unique function of least $ {H^2}$ norm in $ C({c_1}, \ldots ,{c_n})$ is explicitly determined.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507325-8
Keywords: Positive real part, $ {H^2}$, minimal interpolation, Riesz-Herglotz representation, coefficient body, multiplier rule
Article copyright: © Copyright 1978 American Mathematical Society