Partial sums of orthonormal bases preserving positivity—And martingales
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We characterize, for finite measure spaces, those orthonormal bases with the following positivity property: if f is a non-negative function, then the partial sums in the expansion of f are non-negative. The bases are necessarily generalized Haar functions and the partial sums are a martingale closed on the right by f.
Math Subject ClassificationsPrimary 42C10 42C20 secondary 60G46
Keywords and PhrasesHaar series martingale sums
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