Shohat–Favard type theorem for orthogonal series

✍ Scribed by Jeannette Van Iseghem

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 200 KB
• Volume: 219
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.05.020

✦ Synopsis

A function f is considered in the form of its formal series expansion ∞ k=0 f k P k where (P k ) ∞ k=0 denotes a given system of orthogonal polynomials with respect to a measure on the real line. We prove that the denominators, numerators and residuals of their Frobenius-Padé approximation satisfy a five-term recurrence relation. The converse result is obtained: starting from the sequence of denominators, the function f is reconstructed, i.e. the analogous of the classical Shohat-Favard theorem is done.