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

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.


Published in:
Journal of Approximation Theory, 189, 137-159
Year:
2015
Publisher:
San Diego, Elsevier
ISSN:
0021-9045
Keywords:
Laboratories:




 Record created 2014-11-11, last modified 2018-03-13


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