Sparse subsets of orthonormal systems

Price, J. J.

doi:10.1090/S0002-9939-1972-0301439-8

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Sparse subsets of orthonormal systems
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by J. J. Price PDF

Proc. Amer. Math. Soc. 35 (1972), 161-164 Request permission

Abstract:

There exist families of Walsh, Haar and trigonometric functions that have density zero and yet are complete in the sense of measure.

References

Casper Goffman and Daniel Waterman, Basic sequences in the space of measurable functions, Proc. Amer. Math. Soc. 11 (1960), 211–213. MR 112028, DOI 10.1090/S0002-9939-1960-0112028-4
J. J. Price, A density theorem for Walsh functions, Proc. Amer. Math. Soc. 18 (1967), 209–211. MR 209760, DOI 10.1090/S0002-9939-1967-0209760-7
J. J. Price and Robert E. Zink, On sets of completeness for families of Haar functions, Trans. Amer. Math. Soc. 119 (1965), 262–269. MR 184023, DOI 10.1090/S0002-9947-1965-0184023-X