Distributional equation for Laguerre–Hahn functionals on the unit circle

✍ Scribed by A. Branquinho; M.N. Rebocho

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 547 KB
• Volume: 233
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.02.031

✦ Synopsis

Let u be a Hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carathéodory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for F , zAF = BF 2 + CF + D, and a distributional equation for u, D(Au) = Bu 2 + Cu+ HL, where L is the Lebesgue functional, and the polynomials B, C, H are defined in terms of the polynomials A, B, C , D.