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On the Fourier Constants of a Bounded Function

Published online by Cambridge University Press:  24 October 2008

S. Verblunsky
S. Verblunsky
Affiliation:
Magdalene College
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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

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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