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Hardy Martingales and Jensen's inequality
Published online by Cambridge University Press:Â 17 April 2009
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Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus đN, where analyticity is defined using a lexicographic order on the dual group â€N. We show how, by using basic properties of orders on â€N, 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].
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- Copyright © Australian Mathematical Society 1997