Partial sums of orthonormal bases preserving positivity—And martingales

  • J. L. Denny
  • C. K. Abbey


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 Classifications

Primary 42C10 42C20 secondary 60G46 

Keywords and Phrases

Haar series martingale sums 


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Copyright information

© Birkhäuser Boston 1998

Authors and Affiliations

  • J. L. Denny
    • 1
  • C. K. Abbey
    • 2
  1. 1.Department of Radiology, Department of MathematicsUniversity of ArizonaTucson
  2. 2.Department of Radiology, Committee on Applied MathematicsUniversity of ArizonaTucson

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