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On the geometric properties of Vandermonde's mapping and on the problem of moments

Published online by Cambridge University Press:  14 November 2011

V. P. Kostov
V. P. Kostov
Affiliation:
Do Vostrebovania, MGU, Leninskie gory, 117234 Moscow, U.S.S.R.
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Synopsis

In this paper we prove that the domain of hyperbolicity of the polynomial xn + λ2nn−2+λ3xn−3+ … + λn,λiϵR intersected by the half-space λ2 ≧ – 1, has the property of Whitney, i.e., every two points of this set can be connected by a piecewise-smooth curve belonging to it, whose length is ≦C times greater than the euclidian distance between the points, where the constant C does not depend on the choice of the points. Parallel with this, we show that the values x1≦x2≦…≦xn of a random variable are uniquely determined by the corresponding probabilities and by thefirst n moments.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 203 - 211
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

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