Partial sums of orthonormal bases preserving positivity—And martingales |
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| Authors: | J. L. Denny C. K. Abbey |
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| Affiliation: | (1) Department of Radiology, Department of Mathematics, University of Arizona, 85721 Tucson, AZ;(2) Department of Radiology, Committee on Applied Mathematics, University of Arizona, 85721 Tucson, AZ |
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| Abstract: | 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. |
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| Keywords: | Primary 42C10 42C20 secondary 60G46 |
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