On two theorems of S. Verblunsky
- 1 January 1950
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 46 (1) , 57-66
- https://doi.org/10.1017/s0305004100025470
Abstract
In connexion with moment problems, S. Verblunsky proved the following two theorems:Theorem I. (a) If f(x) is integrable in (−∞, +∞) and satisfies 0 ≤f(x) ≤ 1, then there exists a function σ(x), bounded and non-decreasing in (−∞, +∞), such that, for ζ = ξ + iη and η ≠ 0,Keywords
This publication has 3 references indexed in Scilit:
- On the initial moments of a bounded functionMathematical Proceedings of the Cambridge Philosophical Society, 1947
- Two moment problems for bounded functionsMathematical Proceedings of the Cambridge Philosophical Society, 1946
- Recherches sur les fractions continuesAnnales de la faculté des sciences de Toulouse Mathématiques, 1894