Extremal problems, inequalities, and classical orthogonal polynomials

Authors:
Ravi P. Agarwal;Gradimir V. Milovanović
Affiliations:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511, Singapore;Department of Mathematics, Faculty of Electronic Engineering, University of Nis, P.O. Box 73, 18000 Nis, Serbia, Yugoslavia
Venue:
Applied Mathematics and Computation - Orthogonal systems and applications
Year:
2002

Citing 2
Cited 1

New inequalities of Markov type

SIAM Journal on Mathematical Analysis
Some weighted polynomial inequalities in L2-norm

Journal of Approximation Theory

Gauss-Hermite interval quadrature rule

Computers & Mathematics with Applications

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Abstract

In this survey paper we give a short account on characterizations for very classical orthogonal polynomials via extremal problems and the corresponding inequalities. Besides the basic properties of the classical orthogonal polynomials, we consider polynomial inequalities of Landau and Kolmogoroff type, some weighted polynomial inequalities in L2-norm of Markov-Bernstein type, as well as the corresponding connections with the classical orthogonal polynomial.