A divergent weighted orthonormal series of broken line Franklin functions
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- by Coke S. Reed PDF
- Trans. Amer. Math. Soc. 192 (1974), 23-28 Request permission
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
- Philip Franklin, A set of continuous orthogonal functions, Math. Ann. 100 (1928), no. 1, 522–529. MR 1512499, DOI 10.1007/BF01448860
- J. L. Sox Jr., A class of complete orthogonal sequences of broken line functions, Trans. Amer. Math. Soc. 166 (1972), 293–296. MR 291720, DOI 10.1090/S0002-9947-1972-0291720-8
- Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg, C. T. C. Wall’s contributions to the topology of manifolds, Surveys on surgery theory, Vol. 1, Ann. of Math. Stud., vol. 145, Princeton Univ. Press, Princeton, NJ, 2000, pp. 3–15. MR 1747526
Additional Information
- © Copyright 1974 American Mathematical Society
- 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