Szeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\’e approximants

dc.contributor.authorAptekarev, Alexander I.
dc.contributor.authorBogolubsky, Alexey I.
dc.contributor.authorYattselev, Maxim I.
dc.contributor.departmentMathematical Sciences, School of Scienceen_US
dc.date.accessioned2018-11-16T19:55:05Z
dc.date.available2018-11-16T19:55:05Z
dc.date.issued2016
dc.description.abstractLet $\widehat\sigma$ 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.versionAuthor's manuscripten_US
dc.identifier.citationAptekarev, 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.urihttps://hdl.handle.net/1805/17778
dc.language.isoenen_US
dc.publisherarXiven_US
dc.relation.journalArXiv E-Printsen_US
dc.rightsPublisher Policyen_US
dc.sourceArXiven_US
dc.subjectFrobenius-Padé approximantsen_US
dc.subjectorthogonal expansionen_US
dc.subjectnumerical analysisen_US
dc.titleSzeg\H{o}-type asymptotics for ray sequences of Frobenius-Pad\’e approximantsen_US
dc.typeArticleen_US
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