Relative asymptotics for general orthogonal polynomials

Simanek, Brian

doi:10.1307/mmj/1488510031

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…In the present work, following B. Simanek (see [5]), we consider a more general condition instead of condition (9): for some fixed ∈ N,…”

Section: Formulation Of Problemmentioning

confidence: 99%

“…In the general case supp( ) ⊂ C, as a generalization of the Jacobi matrix, we can consider Hessenberg matrices, that is, the matrices corresponding to the operator of multiplication by the independent variable in the space 2 ( ) in the basis of the corresponding orthogonal polynomials. It was shown in work [5] by B. Simanek that as supp( ) ⊂ C, condition (1) is equivalent to coinciding of the right limits of the corresponding Hessenberg matrices.…”

Section: Introductionmentioning

confidence: 99%

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On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity

Kononova¹

2018

Ufimskii Matematicheskii Zhurnal

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We consider the influence of the measure perturbations on the asymptotic behavior of the ratio of orthogonal polynomials. We suppose that the absolutely continuous part of the measure is supported on finitely many Jordan curves. The weight function satisfies the modified Szegö condition. The singular part of the measure consists of finitely many point masses outside the polynomial convex hull of the support of the absolutely continuous part of the measure. We study the stability of asymptotics of the ratio in the following sense: , () , +1 () − , () , +1 () → 0, → ∞. The problem is a generalization of the problem on compactness of the perturbation of Jacobi operator generated by the perturbation of its spectral measure. We find a condition necessary (or necessary and sufficient under some additional restriction) for the stability of the asymptotical behavior of the corresponding orthogonal polynomials. One of the main tools in the study are the Riemann theta functions.

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“…In the present work, following B. Simanek (see [5]), we consider a more general condition instead of condition (9): for some fixed ∈ N,…”

Section: Formulation Of Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity

Kononova¹

2018

Ufimskii Matematicheskii Zhurnal

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Comparative asymptotics for discrete semiclassical orthogonal polynomials

Dominici

2022

Bull. Math. Sci.

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We study the ratio [Formula: see text] asymptotically as [Formula: see text] where the polynomials [Formula: see text] are orthogonal with respect to a discrete linear functional and [Formula: see text] denote the falling factorial polynomials. We give recurrences that allow the computation of high order asymptotic expansions of [Formula: see text] and give examples for most discrete semiclassical polynomials of class [Formula: see text] We show several plots illustrating the accuracy of our results.

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Relative asymptotics for general orthogonal polynomials

Cited by 2 publications

References 20 publications

On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity

On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity

Comparative asymptotics for discrete semiclassical orthogonal polynomials

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