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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A class of complete orthogonal sequences of step functions

Authors: J. L. Sox and W. J. Harrington
Journal: Trans. Amer. Math. Soc. 157 (1971), 129-135
MSC: Primary 42.15
MathSciNet review: 0275046
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Abstract: A class of orthogonal sets of step functions is defined and each member is shown to be complete in $ {L_2}(0,1)$. Pointwise convergence theorems are obtained for the Fourier expansions relative to these sets. The classical Haar orthogonal set is shown to be a set of this class and the class itself is seen to be a subclass of the ``generalized Haar systems'' defined recently by Price.

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

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  • [3] J. J. Price, An algebraic characterization of certain orthonormal systems, Proc. Amer. Math. Soc. 19 (1968), 268-273. MR 37 #682. MR 0225085 (37:682)
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Keywords: Haar functions, Fourier analysis, orthonormal set of functions, complete in $ {L_2}(0,1)$, pointwise convergence, generalized Haar system
Article copyright: © Copyright 1971 American Mathematical Society

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