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Proceedings of the American Mathematical Society

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Sparse subsets of orthonormal systems


Author: J. J. Price
Journal: Proc. Amer. Math. Soc. 35 (1972), 161-164
MSC: Primary 42A52
DOI: https://doi.org/10.1090/S0002-9939-1972-0301439-8
MathSciNet review: 0301439
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Abstract: There exist families of Walsh, Haar and trigonometric functions that have density zero and yet are complete in the sense of measure.


References [Enhancements On Off] (What's this?)

  • [1] C. Goffman and D. Waterman, Basic sequences in the space of measurable functions, Proc. Amer. Math. Soc. 11 (1960), 211-213. MR 22 #2886. MR 0112028 (22:2886)
  • [2] J. J. Price, A density theorem for Walsh functions, Proc. Amer. Math. Soc. 18 (1967), 209-211. MR 35 #656. MR 0209760 (35:656)
  • [3] J. J. Price and R. E. Zink, On sets of completeness for families of Haar functions, Trans. Amer. Math. Soc. 119 (1965), 262-269. MR 32 #1499. MR 0184023 (32:1499)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0301439-8
Keywords: Walsh functions, Haar functions, total in measure
Article copyright: © Copyright 1972 American Mathematical Society

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