Convergence of two-point Padé approximants to piecewise holomorphic functions
dc.contributor.author | Yattselev, M. L. | |
dc.contributor.department | Mathematical Sciences, School of Science | en_US |
dc.date.accessioned | 2023-05-15T17:17:34Z | |
dc.date.available | 2023-05-15T17:17:34Z | |
dc.date.issued | 2021-11 | |
dc.description.abstract | Let $f_0$ and $f_\infty$ be formal power series at the origin and infinity, and $P_n/Q_n$, $\deg(P_n),\deg(Q_n)\leq n$, be the rational function that simultaneously interpolates $f_0$ at the origin with order $n$ and $f_\infty$ at infinity with order ${n+1}$. When germs $f_0$ and $f_\infty$ represent multi-valued functions with finitely many branch points, it was shown by Buslaev that there exists a unique compact set $F$ in the complement of which the approximants converge in capacity to the approximated functions. The set $F$ may or may not separate the plane. We study uniform convergence of the approximants for the geometrically simplest sets F that do separate the plane. | en_US |
dc.eprint.version | Author's manuscript | en_US |
dc.identifier.citation | Yattselev, M. L. (2021). Convergence of two-point Padé approximants to piecewise holomorphic functions. Sbornik: Mathematics, 212(11), 1626–1659. https://doi.org/10.1070/SM9024 | en_US |
dc.identifier.issn | 1064-5616 | en_US |
dc.identifier.uri | https://hdl.handle.net/1805/32981 | |
dc.language.iso | en_US | en_US |
dc.publisher | IOP | en_US |
dc.relation.isversionof | 10.1070/SM9024 | en_US |
dc.relation.journal | Sbornik: Mathematics | en_US |
dc.rights | Publisher Policy | en_US |
dc.source | ArXiv | en_US |
dc.subject | two-point Padé approximants | en_US |
dc.subject | holomorphic functions | en_US |
dc.subject | Stahl's theorem | en_US |
dc.title | Convergence of two-point Padé approximants to piecewise holomorphic functions | en_US |
dc.type | Article | en_US |
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