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A Rakhmanov-like theorem for orthogonal polynomials on Jordan arcs in the complex plane

机译:复平面上约旦弧上正交多项式的Rakhmanov类定理

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摘要

Rakhmanov's theorem establishes a result about the asymptotic behavior of the elements of the Jacobi matrix associated with a measure ¹ which is de¯ned on the interval I = [¡1; 1] with ¹ 0 > 0 almost everywhere on I. In this work we give a weak version of this theorem, for a measure with support on a connected ¯nite union of Jordan arcs on the complex plane, in terms of the Hessenberg matrix, the natural generalization of the tridiagonal Jacobi matrix to the complex plane.
机译:拉赫曼诺夫定理建立了一个关于雅可比矩阵元素与量度“ 1”相关联的渐进行为的结果,该量度在区间I = [¡1; 1]在I上几乎到处都存在¹0> 0。三对角雅可比矩阵对复平面的自然泛化。

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