Name
Abstract | ||
|---|---|---|
Let {α1, α2,...} be a sequence of real numbers outside the interval [-1, 1] and µ a positive bounded Borel measure on this interval satisfying the Erdös-Turán condition µ' 0 a.e., where µ' is the Radon-Nikodym derivative of the measure µ with respect to the Lebesgue measure. We introduce rational functions φn(x) with poles {α1, ..., αn} orthogonal on [-1, 1] and establish some ratio asymptotics for these orthogonal rational functions, i.e. we discuss the convergence of φn-1(x)/φn(x) as n tends to infinity under certain assumptions on the location of the poles. From this we derive asymptotic formulas for the recurrence coefficients in the three-term recurrence relation satisfied by the orthonormal functions. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0021-9045(03)00116-3 | Journal of Approximation Theory |
Keywords | Field | DocType |
asymptotic formula,certain assumption,ratio asymptotics,positive bounded borel measure,lebesgue measure,three-term recurrence relation,orthogonal polynomials,orthogonal rational functions,recurrence coefficient,n condition,orthogonal rational function,orthonormal function,rational function,orthogonal polynomial,borel measure,recurrence relation | Borel measure,Orthogonal functions,Combinatorics,Mathematical analysis,Recurrence relation,Lebesgue measure,Orthonormal basis,Rational function,Real number,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
123 | 2 | 0021-9045 |
Citations | PageRank | References |
3 | 0.76 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. Van Deun | 1 | 10 | 1.65 |
| A. Bultheel | 2 | 117 | 17.02 |