Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 507325
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] M. R. Hestenes, Calculus of variations and optimal control theory, Wiley, New York, 1966. MR 0203540 (34:3390)
  • [2] A. Pfluger, Some coefficient problems of starlike functions, Ann. Acad. Sci. Fenn. Ser. AI 2 (1976), 383-396. MR 0492213 (58:11359)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D50

Retrieve articles in all journals with MSC: 30D50

Additional Information

Keywords: Positive real part, $ {H^2}$, minimal interpolation, Riesz-Herglotz representation, coefficient body, multiplier rule
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society