Nonnegative Quadratic Forms and Bounds on Orthogonal Polynomials

Author: Krasikov I.

Source: Journal of Approximation Theory, Volume 111, Number 1, July 2001 , pp. 31-49(19)

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Abstract:

We show that some nonnegative quadratic forms containing orthogonal polynomials, such as e.g. the Christoffel–Darboux kernel for x=y in the classical case, provide a lot of information about behavior of the polynomials on the real axis. We illustrate the method for the case of Hermite polynomials and use it to derive new explicit bounds for binary Krawtchouk polynomials. Copyright 2001 Academic Press.

Keywords: orthogonal polynomials; Hermite polynomials; Krawtchouk polynomials; bounds

Language: English

Document Type: Research article

Affiliations: Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, United Kingdom

Publication date: 2001-07-01