Shohat–Favard type theorem for orthogonal series
| Autor: | Jeannette Van Iseghem |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Shohat–Favard theorem
Recurrence relation Orthogonal polynomials Applied Mathematics Function (mathematics) Frobenius–Padé approximants Combinatorics Computational Mathematics Rational approximation Orthogonal series Padé approximant Function composition Series expansion Real line Incidence (geometry) Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 219(2):537-550 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2007.05.020 |
| Popis: | A function f is considered in the form of its formal series expansion @?"k"="0^~f"kP"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-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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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