A simple proof of Livingston’s inequality for Carathéodory functions
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- by Philippe Delsarte and Yves Genin PDF
- Proc. Amer. Math. Soc. 107 (1989), 1017-1020 Request permission
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
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N. I. Akhiezer, The classical moment problem, Oliver and Boyd, London, 1965.
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Additional 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