On smooth perturbations of Chebyshëv polynomials and $ \bar {\partial } $-Riemann–Hilbert method
Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 142-155
Voir la notice de l'article provenant de la source Cambridge
$\bar {\partial } $-extension of the matrix Riemann–Hilbert method is used to study asymptotics of the polynomials $ P_n(z) $ satisfying orthogonality relations $$ \begin{align*} \int_{-1}^1 x^lP_n(x)\frac{\rho(x)dx}{\sqrt{1-x^2}}=0, \quad l\in\{0,\ldots,n-1\}, \end{align*} $$where $ \rho (x) $ is a positive $ m $ times continuously differentiable function on $ [-1,1] $, $ m\geq 3 $.
Mots-clés :
Orthogonal polynomials, strong asymptotics, matrix Riemann–Hilbert approach
Yattselev, Maxim L. On smooth perturbations of Chebyshëv polynomials and $ \bar {\partial } $-Riemann–Hilbert method. Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 142-155. doi: 10.4153/S0008439522000145
@article{10_4153_S0008439522000145,
author = {Yattselev, Maxim L.},
title = {On smooth perturbations of {Chebysh\"ev} polynomials and $ \bar {\partial } ${-Riemann{\textendash}Hilbert} method},
journal = {Canadian mathematical bulletin},
pages = {142--155},
year = {2023},
volume = {66},
number = {1},
doi = {10.4153/S0008439522000145},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000145/}
}
TY - JOUR
AU - Yattselev, Maxim L.
TI - On smooth perturbations of Chebyshëv polynomials and $ \bar {\partial } $-Riemann–Hilbert method
JO - Canadian mathematical bulletin
PY - 2023
SP - 142
EP - 155
VL - 66
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000145/
DO - 10.4153/S0008439522000145
ID - 10_4153_S0008439522000145
ER -
%0 Journal Article
%A Yattselev, Maxim L.
%T On smooth perturbations of Chebyshëv polynomials and $ \bar {\partial } $-Riemann–Hilbert method
%J Canadian mathematical bulletin
%D 2023
%P 142-155
%V 66
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000145/
%R 10.4153/S0008439522000145
%F 10_4153_S0008439522000145
Cité par Sources :