On Perfectness of Systems of Weights Satisfying Pearson’s Equation with Nonstandard Parameters

Author:

Aptekarev Alexander,Dyachenko Alexander,Lysov Vladimir

Abstract

Measures generating classical orthogonal polynomials are determined by Pearson’s equation, whose parameters usually provide the positivity of the measures. The case of general complex parameters (nonstandard) is also of interest; the non-Hermitian orthogonality with respect to (now complex-valued) measures is considered on curves in C. Some applications lead to multiple orthogonality with respect to a number of such measures. For a system of r orthogonality measures, the perfectness is an important property: in particular, it implies the uniqueness for the whole family of corresponding multiple orthogonal polynomials and the (r+2)-term recurrence relations. In this paper, we introduce a unified approach which allows to prove the perfectness of the systems of complex measures satisfying Pearson’s equation with nonstandard parameters. We also study the polynomials satisfying multiple orthogonality relations with respect to a system of discrete measures. The well-studied families of multiple Charlier, Krawtchouk, Meixner and Hahn polynomials correspond to the systems of measures defined by the difference Pearson’s equation with standard real parameters. Using the same approach, we verify the perfectness of such systems for general parameters. For some values of the parameters, discrete measures should be replaced with the continuous measures with non-real supports.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference50 articles.

1. Sur la fonction exponentielle;Hermite;C. R. Acad. Sci. Paris Sér. I Math.,1873

2. Multiple orthogonal polynomials, irrationality and transcendence;Berndt;Continued Fractions: From Analytic Number Theory to Constructive Approximation,1999

3. Cyclic graphs and Apéry’s theorem;Sorokin;Russ. Math. Surv.,2002

4. On Salikhov’s integral;Sorokin;Trans. Moscow Math. Soc.,2016

5. Vectors of type II Hermite-Padé approximations and a new linear independence criterion;Marcovecchio;Ann. Mat. Pura Appl.,2021

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