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APPLICATIONS OF AN INTERSECTION FORMULA TO DUAL CONES

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  17 October 2017

DÁNIEL VIROSZTEK
DÁNIEL VIROSZTEK*
Affiliation:
Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary MTA-DE ‘Lendület’ Functional Analysis Research Group, Institute of Mathematics, University of Debrecen, PO Box 400, H-4002 Debrecen, Hungary email [email protected]
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Abstract

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We give a succinct proof of a duality theorem obtained by Révész [‘Some trigonometric extremal problems and duality’, J. Aust. Math. Soc. Ser. A 50 (1991), 384–390] which concerns extremal quantities related to trigonometric polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach spaces. We show another application of this intersection formula which is related to integral estimates of nonnegative positive-definite functions.

Keywords

dualitypositive-definite functionintersection formula

MSC classification

Primary: 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
Secondary: 43A35: Positive definite functions on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 94 - 101
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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