Abstract
Markov’s inequality for algebraic polynomials on \(\left[ -1,1\right] \) goes back to more than a century and it is widely used in approximation theory. Its asymptotically sharp form for unions of finitely many intervals has been found only in 2001 by the third author. In this paper we extend this asymptotic form to arbitrary compact subsets of the real line satisfying an interval condition. With the same method a sharp local version of Schur’s inequality is given for such sets.
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Acknowledgments
Sergei Kalmykov was supported by the European Research Council Advanced Grant No. 267055, while he had a postdoctoral position at the Bolyai Institute, University of Szeged, Aradi v. tere 1, Szeged 6720, Hungary. Béla Nagy was supported by Magyary scholarship: this research was realized in the frames of TÁMOP 4.2.4. A/2-11-1-2012-0001 “National Excellence Program-Elaborating and operating an inland student and researcher personal support system”. The project was subsidized by the European Union and co-financed by the European Social Fund. Vilmos Totik was supported by NSF grant DMS-1265375.
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Communicated by Laurent Baratchart.
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Kalmykov, S., Nagy, B. & Totik, V. Asymptotically Sharp Markov and Schur Inequalities on General Sets. Complex Anal. Oper. Theory 9, 1287–1302 (2015). https://doi.org/10.1007/s11785-014-0405-z
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DOI: https://doi.org/10.1007/s11785-014-0405-z