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Browsing by Author "Yattselev, M. L."
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Item Convergence of two-point Padé approximants to piecewise holomorphic functions(IOP, 2021-11) Yattselev, M. L.; Mathematical Sciences, School of ScienceLet $f_0$ 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.Item On Multipoint Padé Approximants whose Poles Accumulate on Contours that Separate the Plane(Springer, 2021-11) Yattselev, M. L.; Mathematical Sciences, School of ScienceIn this note we consider asymptotics of the multipoint Padé approximants to Cauchy integrals of analytic non-vanishing densities defined on a Jordan arc connecting -1 and 1. We allow for the situation where the (symmetric) contour attracting the poles of the approximants does separate the plane.