On the Sharp Inequalities for Orthonormal Polynomials Along a Contour

ABDULLAYEV F., Abdullayev G.

Complex Analysis and Operator Theory, vol.11, no.7, pp.1569-1586, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 7
  • Publication Date: 2017
  • Doi Number: 10.1007/s11785-017-0640-1
  • Journal Name: Complex Analysis and Operator Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1569-1586
  • Keywords: Algebraic polynomials, Conformal mapping, Orthonormal polynomials, Quasicircle
  • Uşak University Affiliated: No

Abstract

In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the weight functions have some singularities. In particular, we obtain new exact estimations for the growth of the modulus of orthogonal polynomials.