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This article is cited in 1 scientific paper (total in 1 paper)
Convergence of two-point Padé approximants to piecewise holomorphic functions
M. L. Yattselevab a Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN, USA
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia
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.
Bibliography: 26 titles.
Keywords:
two-point Padé approximants, non-Hermitian orthogonality, strong asymptotics, $S$-contours, matrix Riemann-Hilbert approach.
Received: 24.10.2017 and 27.04.2021
Citation:
M. L. Yattselev, “Convergence of two-point Padé approximants to piecewise holomorphic functions”, Sb. Math., 212:11 (2021), 1626–1659
Linking options:
https://www.mathnet.ru/eng/sm9024https://doi.org/10.1070/SM9024 https://www.mathnet.ru/eng/sm/v212/i11/p128
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Abstract page: | 299 | Russian version PDF: | 44 | English version PDF: | 25 | Russian version HTML: | 105 | References: | 42 | First page: | 11 |
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