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Transactions of the American Mathematical Society

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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
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.

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

  • [1] Philip Franklin, A set of continuous orthogonal functions, Math. Ann. 100 (1928), 522-529. MR 1512499
  • [2] J. L. Sox, Jr., A class of complete orthogonal sequences of broken line functions, Trans. Amer. Math. Soc. 166 (1972), 293-296. MR 45 #811. MR 0291720 (45:811)
  • [3] H. S. Wall, Creative mathematics, Univ. of Texas Press, Austin, Tex., 1963, pp. 161-168. MR 1747526

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Keywords: Franklin functions, Fourier series, weighted orthonormal series, broken line functions
Article copyright: © Copyright 1974 American Mathematical Society

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