论文标题
关于Chebyshëv多项式和$ \ bar \ partial $ -riemann-Hilbert方法的平稳扰动
On Smooth Perturbations of Chebyshëv Polynomials and $\bar\partial$-Riemann-Hilbert Method
论文作者
论文摘要
$ \ bar \ partial $ - 矩阵riemann-hilbert方法的extension用于研究多项式$ p_n（z）$满足正交性关系\ [\ int _ { - 1}^1^1 x^lp_n（x）\ frac {ρ（x）dx} {\ sqrt {1-x^2}} = 0，\ quad l \ in \ in \ {0，\ ldots，n-1 \}，n-1 \}，\]，$ρ（x）$是$ m $ m $ $ m $ $ $ $ $ $ $ $ $ $ $ time ge qe $ $ $ $ $ $ $ $ $ $ $ $ $ n-11 n-11 n-11 n-11 n-11 n-11 n-11 n-11 n-11 n-11 n-11。
$\bar\partial$-extension of the matrix Riemann-Hilbert method is used to study asymptotics of the polynomials $P_n(z)$ satisfying orthogonality relations \[ \int_{-1}^1 x^lP_n(x)\frac{ρ(x)dx}{\sqrt{1-x^2}}=0, \quad l\in\{0,\ldots,n-1\}, \] where $ρ(x)$ is a positive $m$ times continuously differentiable function on $[-1,1]$, $m\geq3$.
