Geodesic
On Markov's theorem for multipoint Padé approximants
Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 449-459 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the degree of convergence of interpolating sequences of rational functions (with free poles) for functions of the form $\widehat\mu=\mu*\frac1z$, where $\mu$ is a positive measure with compact support on the real line. Bibliography: 11 titles. 
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     title = {On {Markov's} theorem for multipoint {Pad\'e} approximants},
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     number = {4},
     language = {en},
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A. A. Gonchar; G. López Lagomasino. On Markov's theorem for multipoint Padé approximants. Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 449-459. http://geodesic.mathdoc.fr/item/SM_1978_34_4_a2/

[1] A. A. Markov, Izbrannye trudy po teorii nepreryvnykh drobei i teorii funktsii, naimenee uklonyayuschikhsya ot nulya, Gostekhizdat, Moskva, 1948 | MR

[2] O. Perron, Die Lehre von den Kettenbruchen, Band II, Teubner, Stuttgart, 1957 | MR | Zbl

[3] G. Cere, Ortogonalnye mnogochleny, Fizmatgiz, Moskva, 1962

[4] W. B. Gragg, “Truncation error bounds for $g$-fractions”, Numerische Math., 11 (1968), 370–379 | DOI | MR | Zbl

[5] J. Karlsson and Bjorn von Sydow, “The convergence of Padé approximants to series of Stieltjes”, University of Umea, 1974, no. 6

[6] A. A. Gonchar, “O skhodimosti obobschennykh approksimatsii Pade meromorfnykh funktsii”, Matem. sb., 98(140) (1975), 564–578

[7] M. Barnsley, “The bounding properties of the multipoint Padé approximant to a series of Stieltjes on the real line”, J. Math. Phys., 14:3 (1973), 299–313 | DOI | MR | Zbl

[8] A. A. Gonchar, “O skorosti ratsionalnoi approksimatsii nekotorykh analiticheskikh, funktsii”, Matem. sb., 105(147) (1978), 147–163 | MR | Zbl

[9] J. Karlsson, “Rational interpolation and best rational approximation”, J. Math. Anal. Appl., 53:1 (1976), 38–51 | DOI | MR

[10] Dzh. L. Uolsh, Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, Moskva, 1961 | MR

[11] T. Bagby, “On interpolation by rational functions”, Duke Math. J., 36:1 (1969), 95–104 | DOI | MR | Zbl