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A Tangential Markov Inequality on Exponential Curves

L. P. Bos·A. Brudnyi·N. Levenberg
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Abstract

We show that on the curves y=e^{t(x)} where t(x) is a fixed polynomial, there holds a tangential Markov inequality of exponent four. Specifically, for the real interval [a,b] there is a constant C such that max_{x\in [a,b]}|\frac{d}{dx}P(x,e^{t(x)})|\leq C(deg(P))^{4} max_{x\in [a,b]}|P(x,e^{t(x)})| for all bivariate polynomials P(x,y).

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L. P. Bos, A. Brudnyi, N. Levenberg. 2001-04-25. A Tangential Markov Inequality on Exponential Curves. https://arxiv.org/abs/math/0104238

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