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Tangential Markov Inequalities on Transcendental Curves |
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| Authors: | Bos Brudnyi Levenberg Totik |
| Affiliation: | Department of Mathematics and Statistics University of Calgary Calgary Alberta Canada T2N 1N4, CA Department of Mathematics and Statistics University of Calgary Calgary Alberta Canada T2N 1N4, CA Department of Mathematics University of Auckland Private Bag 92019 Auckland New Zealand, NZ Bolyai Institute University of Szeged Hungary, HU |
| Abstract: | Abstract. We show that on the curves γ:=(x,e t(x) ) , x∈ [a,b] , where t(x) is a fixed polynomial, there holds a tangential Markov inequality of exponent four for algebraic polynomials P N (x,y) of degree at most N in each variable x,y: ||(P N (x,e t(x) ))'|| [a,b] ≤ CN 4 ||P N || γ , and the exponent four is sharp. On the other hand, the corresponding tangential Markov factors on curves y=x α with irrational α grow exponentially in the degree of the polynomials. |
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