Shohat-Favard type theorem for orthogonal series

[摘要] A function f is considered in the form of its formal series expansion E-k=0(infinity) f(k) P-k where (P-k)(k=0)(infinity) 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-Pade 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. (C) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2008-10-01

[效力级别]  Proceedings Paper

[关键词] rational approximation;orthogonal polynomials;orthogonal series;Frobenius-Pade approximants;Shohat-Favard theorem