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    Khrushchev, S.V. 2002. Classification Theorems for General Orthogonal Polynomials on the Unit Circle. Journal of Approximation Theory, Vol. 116, Issue. 2, p. 268.
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On the Fourier Constants of a Bounded Function

  • S. Verblunsky (a1)
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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

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COPYRIGHT: © Cambridge Philosophical Society 1936
References
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* “Solution of a moment problem for bounded functions”, Proc. Camb. Phil. Soc. 32 (1936), 30–39. This paper will be referred to as I.

* For a proof see Verblunsky, , Proc. London Math. Soc. (2), 37 (1933), 33–62 (34).

* 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.

‡ Fejér, , Math. Annalen, 97 (1926), 104–23.

§ Schur, , J. für Math. 147 (1917), 205–32.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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