On the Fourier Constants of a Bounded Function
Published online by Cambridge University Press: 24 October 2008
Extract
1. In a former paper we solved the following problem (Problem I). Given k + 1 real numbers co, …, ck, to find necessary and sufficient conditions that there shall exist a function f(x) in (0, 1) which satisfies the conditions
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 32 , Issue 2 , May 1936 , pp. 201 - 211
- Copyright
- Copyright © Cambridge Philosophical Society 1936
References
* “Solution of a moment problem for bounded functions”, Proc. Camb. Phil. Soc. 32 (1936), 30–39.CrossRefGoogle Scholar This paper will be referred to as I.
* For a proof see Verblunsky, , Proc. London Math. Soc. (2), 37 (1933), 33–62 (34).Google Scholar
* This means “necessary and sufficient in order that (40) shall hold for all polynomials of degree not greater than k”. Similar interpretations are to be given at every subsequent mention of (40).
† Carathéodory, and Fejér, , Rend. di Palermo, 32 (1911), 218–39.CrossRefGoogle Scholar
‡ Fejér, , Math. Annalen, 97 (1926), 104–23.CrossRefGoogle Scholar
§ Schur, , J. für Math. 147 (1917), 205–32.Google Scholar
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