A simple proof of Livingston’s inequality for Carathéodory functions
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- by Philippe Delsarte and Yves Genin
- Proc. Amer. Math. Soc. 107 (1989), 1017-1020
- DOI: https://doi.org/10.1090/S0002-9939-1989-0984785-7
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Abstract:
The Livingston determinant inequality involving the Maclaurin coefficients of a Carathéodory function are derived in a straightforward manner by use of the Riesz-Herglotz representation and the Schwarz inequality. The result is extended to the case of matrix-valued functions.References
- N. I. Akhiezer, The classical moment problem, Oliver and Boyd, London, 1965.
- Philippe Delsarte, Yves V. Genin, and Yves G. Kamp, Orthogonal polynomial matrices on the unit circle, IEEE Trans. Circuits and Systems CAS-2 (1978), no. 3, 149–160. MR 481886, DOI 10.1109/TCS.1978.1084452
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- Albert E. Livingston, A coefficient inequality for functions of positive real part with an application to multivalent functions, Pacific J. Math. 120 (1985), no. 1, 139–151. MR 808934, DOI 10.2140/pjm.1985.120.139
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 1017-1020
- MSC: Primary 30C50; Secondary 30D50
- DOI: https://doi.org/10.1090/S0002-9939-1989-0984785-7
- MathSciNet review: 984785