Estimates for Norms of Random Polynomials

Details Estimates for Norms of Random Polynomials Estimates for Norms of Random Polynomials

2002-10-22

arxiv.org/abs/math/0210342v1

East Journal of Approximation 2001 v. 7 no. 4 pp.445--469

Mathematics

Probability

Almost the same text was published in East J. Approximation 2001 v. 7 no. 4 pp. 445--469

Scientific paper

This paper contains some estimates for the {\it integral-uniform} norm and the uniform norm of a wide class of random polynomials. The family of integral-uniform norms introduced by Kasin and Tzafriri is a natural generalization of the maximum norm taken over a net. We prove some properties of the integral-uniform norms. The given application of the established estimates demonstrates that the integral-uniform norms may be useful whenever one is interested in the properties of a function distribution. Key words: integral-uniform norm; random polynomials with respect to a general function system; trigonometric polynomials with random coefficients.

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