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On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity. / Kononova, Anna Alexandrovna.

In: Ufa Mathematical Journal, Vol. 10, No. 1, 01.01.2018, p. 64-75.

Research output: Contribution to journal › Article › peer-review

Harvard

Kononova, AA 2018, 'On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity', Ufa Mathematical Journal, vol. 10, no. 1, pp. 64-75. https://doi.org/10.13108/2018-10-1-64

APA

Kononova, A. A. (2018). On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity. Ufa Mathematical Journal, 10(1), 64-75. https://doi.org/10.13108/2018-10-1-64

Vancouver

Kononova AA. On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity. Ufa Mathematical Journal. 2018 Jan 1;10(1):64-75. https://doi.org/10.13108/2018-10-1-64

Author

Kononova, Anna Alexandrovna. / On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity. In: Ufa Mathematical Journal. 2018 ; Vol. 10, No. 1. pp. 64-75.

BibTeX

@article{e6f48e2ef764450aa831be7f5159fcc1,
title = "On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity",
abstract = "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 Szeg{\"o} 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: Pv,n(Z)/Pv,n+1(Z) - Pv,n(Z)/Pv,n+1(Z) → 0, n → ∞. 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.",
keywords = "Multivalued functions, Orthogonal polynomials",
author = "Kononova, {Anna Alexandrovna}",
year = "2018",
month = jan,
day = "1",
doi = "10.13108/2018-10-1-64",
language = "English",
volume = "10",
pages = "64--75",
journal = "Ufa Mathematical Journal",
issn = "2304-0122",
publisher = "Institute of Mathematics with Computer Center of Russian Academy of Sciences",
number = "1",

}

RIS

TY - JOUR

T1 - On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity

AU - Kononova, Anna Alexandrovna

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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: Pv,n(Z)/Pv,n+1(Z) - Pv,n(Z)/Pv,n+1(Z) → 0, n → ∞. 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.

AB - 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: Pv,n(Z)/Pv,n+1(Z) - Pv,n(Z)/Pv,n+1(Z) → 0, n → ∞. 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.

KW - Multivalued functions

KW - Orthogonal polynomials

UR - http://www.scopus.com/inward/record.url?scp=85044312075&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=32705553

U2 - 10.13108/2018-10-1-64

DO - 10.13108/2018-10-1-64

M3 - Article

AN - SCOPUS:85044312075

VL - 10

SP - 64

EP - 75

JO - Ufa Mathematical Journal

JF - Ufa Mathematical Journal

SN - 2304-0122

IS - 1

ER -

ID: 15769202