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Hardy Martingales and Jensen's inequality

Published online by Cambridge University Press:  17 April 2009

Nakhlé H. Asmar  and
Stephen J. Montgomery-Smith
Nakhlé H. Asmar
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, MI 65211, United States of America
Stephen J. Montgomery-Smith
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, MI 65211, United States of America
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Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus 𝕋N, where analyticity is defined using a lexicographic order on the dual group ℤN. We show how, by using basic properties of orders on ℤN, we can apply Garling's method in the study of analytic functions on an arbitrary compact Abelian group with an arbitrary order on its dual group. We illustrate our approach by giving a new and simple proof of a famous generalised Jensen's Inequality due to Helson and Lowdenslager[5].

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 185 - 195
Copyright
Copyright © Australian Mathematical Society 1997

References

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