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On Some Property of Convex Functions and an Inequality for the Vandermonde Determinants

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Abstract

An inequality for the Vandermonde determinants is proved. In particular, the results confirm the conjecture suggested in [J. Math. Sci. 117 (2003), No. 3] about the extremal property of the so-called Euler integrated processes. Bibliography: 2 titles.

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References

  1. A. I. Nazarov, “On the sharp constant in the small ball asymptotics of some Gaussian processes under L 2-norm” [in Russian], Probl. Mat. Anal., 26, (2003), 179–214; English transl.: J. Math. Sci., 117 (2003), No. 3, 4185–4210.

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  2. M. J. Hadamard. “Résolution d'une question relative aux déterminants,” Bull. Sci. Math., 17 (1893), No 1, 240–246.

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Authors
  1. A. I. Nazarov
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  2. F. L. Nazarov
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Nazarov, A.I., Nazarov, F.L. On Some Property of Convex Functions and an Inequality for the Vandermonde Determinants. Journal of Mathematical Sciences 120, 1122–1124 (2004). https://doi.org/10.1023/B:JOTH.0000014841.92050.fe

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  • DOI: https://doi.org/10.1023/B:JOTH.0000014841.92050.fe

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