Szeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\’e approximants
dc.contributor.author | Aptekarev, Alexander I. | |
dc.contributor.author | Bogolubsky, Alexey I. | |
dc.contributor.author | Yattselev, Maxim I. | |
dc.contributor.department | Mathematical Sciences, School of Science | en_US |
dc.date.accessioned | 2018-11-16T19:55:05Z | |
dc.date.available | 2018-11-16T19:55:05Z | |
dc.date.issued | 2016 | |
dc.description.abstract | Let $\widehat\sigma$ be a Cauchy transform of a possibly complex-valued Borel measure $\sigma$ and $\{p_n\}$ be a system of orthonormal polynomials with respect to a measure $\mu$, $\mathrm{supp}(\mu)\cap\mathrm{supp}(\sigma)=\varnothing$. An $(m,n)$-th Frobenius-Pad\'e approximant to $\widehat\sigma$ is a rational function $P/Q$, $\mathrm{deg}(P)\leq m$, $\mathrm{deg}(Q)\leq n$, such that the first $m+n+1$ Fourier coefficients of the linear form $Q\widehat\sigma-P$ vanish when the form is developed into a series with respect to the polynomials $p_n$. We investigate the convergence of the Frobenius-Pad\'e approximants to $\widehat\sigma$ along ray sequences $\frac n{n+m+1}\to c>0$, $n-1\leq m$, when $\mu$ and $\sigma$ are supported on intervals on the real line and their Radon-Nikodym derivatives with respect to the arcsine distribution of the respective interval are holomorphic functions. | en_US |
dc.eprint.version | Author's manuscript | en_US |
dc.identifier.citation | Aptekarev, A. I., Bogolubsky, A. I., & Yattselev, M. L. (2016). Szeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\’e approximants. ArXiv E-Prints, 1605, arXiv:1605.09672. | en_US |
dc.identifier.uri | https://hdl.handle.net/1805/17778 | |
dc.language.iso | en | en_US |
dc.publisher | arXiv | en_US |
dc.relation.journal | ArXiv E-Prints | en_US |
dc.rights | Publisher Policy | en_US |
dc.source | ArXiv | en_US |
dc.subject | Frobenius-Padé approximants | en_US |
dc.subject | orthogonal expansion | en_US |
dc.subject | numerical analysis | en_US |
dc.title | Szeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\’e approximants | en_US |
dc.type | Article | en_US |