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Transactions of the American Mathematical Society
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0275046-3
PII: S 0002-9947(1971)0275046-3
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