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TW 260
P. Verlinden
An asymptotic estimate of Hilb's type for generalized Jacobi polynomials on the unit circle
Abstract
We consider generalized Jacobi weight functions w on the unit circle T, i.e. w is positive and smooth everywhere except at a finite number of points zk ∈ T, such that for small t, w(zk eit) is equal to |t| βk : ( βk > -1) multiplied by some positive smooth function. An asymptotic estimate of Hilb's type is established for the orthogonal polynomials w.r.t. these weight functions. It gives a precise description of the asymptotic behavior of the orthogonal polynomials on the whole unit circle.
report.pdf / mailto: P. Verlinden