Distributional equation for Laguerre-Hahn functionals on the unit circle

[摘要] Let it be a Hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Caratheodory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for F, zAF' = BF2 + CF + D, and a distributional equation for u, D(Au) = (B) over tildeu(2) + (C) over tildeu + (H) over tildeL, where L is the Lebesgue functional, and the polynomials (B) over tilde, (C) over tilde, (H) over tilde are defined in terms of the polynomials A. B. C. D. (C) 2009 Elsevier B.V. All rights reserved.

[发布日期] 2009-12-01

[效力级别]  Proceedings Paper

[关键词] Hermitian functionals;Measures on the unit circle;Caratheodory function;Laguerre-Hahn affine class on the unit circle;Semi-classical functionals