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A simple proof of Livingston's inequality for Carathéodory functions


Authors: Philippe Delsarte and Yves Genin
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0984785-7
Keywords: Carathéodory functions, coefficient inequalities, Riesz-Herglotz representation
Article copyright: © Copyright 1989 American Mathematical Society