Asymptotically Sharp Markov and Schur Inequalities on General Sets

作者：Kalmykov Sergei; Nagy Bela^*; Totik Vilmos

来源：Complex Analysis and Operator Theory, 2015, 9(6): 1287-1302.

DOI：10.1007/s11785-014-0405-z

• Polynomials
• Markov and Schur inequalities
• Sharp constants
• Equilibrium measures

Markov's inequality for algebraic polynomials on 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.

• 出版日期2015-8