Name
Abstract | ||
|---|---|---|
We study diagonal multipoint Pade approximants to functions of theform F(z)=∫ dλ(t) / z-t +R(z), where R is a rational function and λ isa complex measure with compact regular support included inℝ, whose argument has bounded variation on thesupport. Assuming that interpolation sets are such that theirnormalized counting measures converge sufficiently fast in theweak-star sense to some conjugate-symmetric distribution σ,we show that the counting measures of poles of the approximantsconverge to ^σ, the balayage of σ onto the support ofλ, in the weak* sense, that the approximantsthemselves converge in capacity to F outside the support ofλ, and that the poles of R attract at least as many poles ofthe approximants as their multiplicity and not much more. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jat.2008.04.013 | Journal of Approximation Theory |
Keywords | Field | DocType |
non-hermitian orthogonality.,polar singularity,multipoint pad,theform f,conjugate-symmetric distribution,poles ofthe approximants,rational approximation,theweak-star sense,bounded variation,interpolation set,isa complex measure,theirnormalized counting measure,complex cauchy,orthogonal poly- nomials,pad e approximation,compact regular support,approximantsthemselves converge,orthogonal polynomials,pade approximation,rational function | Diagonal,Mathematical optimization,Padé approximant,Orthogonal polynomials,Mathematical analysis,Cauchy distribution,Gravitational singularity,Rational function,Bounded variation,Mathematics,Complex measure | Journal |
Volume | Issue | ISSN |
156 | 2 | J. Approx. Theory, 156(2), 187-211, 2009 |
Citations | PageRank | References |
2 | 0.60 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Baratchart | 1 | 14 | 7.89 |
| Maxim Yattselev | 2 | 4 | 1.22 |