ISSN:
1432-0940

Keywords:
41A17
;
41A10
;
26C05
;
Markov-Bernstein inequalities
;
Polynomials
;
Completeness

Source:
Springer Online Journal Archives 1860-2000

Topics:
Mathematics

Notes:
Abstract For the weights exp (−|x|λ), 0〈λ≤1, we prove the exact analogue of the Markov-Bernstein inequality. The Markov-Bernstein constant turns out to be of order logn for λ=1 and of order 1 for 0〈λ〈1. The proof is based on the solution of the problem of how fast a polynomialP n can decrease on [−1,1] ifP n (0)=1. The answer to this problem has several other consequences in different directions; among others, it leads to a general theorem about the incompleteness of the set of polynomials in weightedL p spaces.

Type of Medium:
Electronic Resource

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