Name
Abstract | ||
|---|---|---|
Let {αk} be a sequence of points on the real axis, and let L denote the linear span of the set {1/ω0;,1/ω1, ...,1/ωn,...}, where ω0 = 1, ωn = (z - α1)(z - α2)... (z - αn) for n ≥ 1. A measure µ with support in an interval [γ, ∞) and with respect to which all functions in L . L are integrable induces an inner product in L and hence orthogonal rational functions {φn} and associated functions {σn} corresponding to the sequence {1/ωn}. Assuming certain constellations of the points {αk}, it is shown that the sequences {-σ2m(z)/φ2m(z)} and {-σ2m+1(z)/ φ2m+1(z)} are monotonic on a certain real interval (α,β) and convergent in the complex plane outside the interval [γ,∞) to functions F(z,µ(0)) and F(z, µ(∞)), where F(z, µ) denotes the Stieltjes transform ∫-∞∞ dµ(t)/(t - z) of a measure µ. Furthermore for every µ giving rise to the same integral values for functions in L . L, the inequality F(x,µ(0)) ≤ F(x,µ) ≤ F(x,µ(∞)) holds for x ∈ (α,β). These results are essentially generalizations of results concerning the strong (or two-point) Stieltjes moment problem, and are also similar to results concerning the classical Stieltjes moment problem. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1016/S0096-3003(01)00073-X | Applied Mathematics and Computation |
Keywords | Field | DocType |
Orthogonal rational functions,Rational moment problems | Monotonic function,Combinatorics,Linear span,Mathematical analysis,Complex plane,Stieltjes moment problem,Function composition,Rational function,Mathematics,Stieltjes transform | Journal |
Volume | Issue | ISSN |
128 | 2-3 | 0096-3003 |
Citations | PageRank | References |
3 | 1.42 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. Bultheel | 1 | 117 | 17.02 |
| P. Gonzalez-Vera | 2 | 15 | 3.58 |
| E. Hendriksen | 3 | 24 | 5.67 |
| Olav NjåStad | 4 | 56 | 12.34 |