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Proceedings of the American Mathematical Society

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Minimal $H^{2}$ 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
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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.

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

  • Magnus R. Hestenes, Calculus of variations and optimal control theory, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0203540
  • Albert Pfluger, Some coefficient problems for starlike functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 2 (1976), 383–396. MR 0492213

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Keywords: Positive real part, <IMG WIDTH="33" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${H^2}$">, minimal interpolation, Riesz-Herglotz representation, coefficient body, multiplier rule
Article copyright: © Copyright 1978 American Mathematical Society