Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

JOURNAL OF APPROXIMATION THEORY

卷:189

Article

Migliorati, Giovanni

关键词: Approximation theory;    Multivariate polynomial approximation;    Markov inequality;    Nikolskii inequality;    Orthogonal polynomials;    Downward closed sets;    Legendre polynomials;    Chebyshev polynomials;    Jacobi polynomials;    Gegenbauer polynomials;   

DOI  :  10.1016/j.jat.2014.10.010

来源: Elsevier

【 摘 要 】

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is expanded in series of tensorized Legendre or Chebyshev or Gegenbauer or Jacobi orthogonal polynomials indexed by a downward closed multi-index set. The proofs of these inequalities rely on a general result concerning the summation of tensorized polynomials over arbitrary downward closed multi-index sets. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free