A Rakhmanov-like theorem for orthogonal polynomials on Jordan arcs in the complex plane
Carmen Escribano, María Asunción Sastre, Antonio Giraldo, E. Torrano · 2010
Rakhmanov’s theorem establishes a result about the asymptotic behavior of the elements of the Jacobi matrix associated with a measure „ which is deflned on the interval I = [i1;1] with „ 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 flnite 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.