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Transactions of the American Mathematical Society

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

 

 

A divergent weighted orthonormal series of broken line Franklin functions


Author: Coke S. Reed
Journal: Trans. Amer. Math. Soc. 192 (1974), 23-28
MSC: Primary 42A56
DOI: https://doi.org/10.1090/S0002-9947-1974-0338672-1
MathSciNet review: 0338672
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Abstract: The purpose of this paper is to define a differentiable function F and an inner product on the space of continuous functions on [0,1] in such a way that the Fourier expansion of F obtained by orthonormalizing the broken line Franklin functions according to this inner product is divergent.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0338672-1
Keywords: Franklin functions, Fourier series, weighted orthonormal series, broken line functions
Article copyright: © Copyright 1974 American Mathematical Society