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Mat. Sb., 2002, Volume 193, Number 12, Pages 105–133 (Mi msb701)  

This article is cited in 14 scientific papers (total in 14 papers)

Approximation properties of the poles of diagonal Padé approximants for certain generalizations of Markov functions

S. P. Suetin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A non-linear system of differential equations (‘`generalized Dubrovin system") is obtained to describe the behaviour of the zeros of polynomials orthogonal on several intervals that lie in lacunae between the intervals. The same system is shown to describe the dynamical behaviour of zeros of this kind for more general orthogonal polynomials: the denominators of the diagonal Padé approximants of meromorphic functions on a real hyperelliptic Riemann surface.
On the basis of this approach several refinements of Rakhmanov’s results on the convergence of diagonal Padé approximants for rational perturbations of Markov functions are obtained.


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English version:
Sbornik: Mathematics, 2002, 193:12, 1837–1866

Bibliographic databases:

UDC: 517.538+517.587
MSC: Primary 41A21, 42C05; Secondary 30F30, 14H40
Received: 21.01.2002 and 14.10.2002

Citation: S. P. Suetin, “Approximation properties of the poles of diagonal Padé approximants for certain generalizations of Markov functions”, Mat. Sb., 193:12 (2002), 105–133; Sb. Math., 193:12 (2002), 1837–1866

Citation in format AMSBIB
\by S.~P.~Suetin
\paper Approximation properties of the poles of diagonal Pad\'e approximants for certain generalizations of Markov functions
\jour Mat. Sb.
\yr 2002
\vol 193
\issue 12
\pages 105--133
\jour Sb. Math.
\yr 2002
\vol 193
\issue 12
\pages 1837--1866

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    This publication is cited in the following articles:
    1. S. P. Suetin, “The asymptotic behaviour of diagonal Padé approximants for hyperelliptic functions of genus $g=2$”, Russian Math. Surveys, 58:4 (2003), 802–804  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. S. P. Suetin, “Convergence of Chebyshëv continued fractions for elliptic functions”, Sb. Math., 194:12 (2003), 1807–1835  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. L. Skorokhodov, “Padé approximation and numerical analysis for the Riemann $\zeta$-function”, Comput. Math. Math. Phys., 43:9 (2003), 1277–1298  mathnet  mathscinet  zmath
    4. A. A. Gonchar, S. P. Suetin, “On Padé Approximants of Meromorphic Functions of Markov Type”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S58–S95  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. S. L. Skorokhodov, “Methods of analytical continuation of the generalized hypergeometric functions $ _pF_{p-1}(a_1,…,a_p;b_1,…,b_{p-1};z)$”, Comput. Math. Math. Phys., 44:7 (2004), 1102–1123  mathnet  mathscinet  zmath
    6. S. P. Suetin, “On polynomials orthogonal on several segments with indefinite weight”, Russian Math. Surveys, 60:5 (2005), 991–993  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. S. P. Suetin, “Comparative Asymptotic Behavior of Solutions and Trace Formulas for a Class of Difference Equations”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S96–S137  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. S. P. Suetin, “Spectral properties of a class of discrete Sturm–Liouville operators”, Russian Math. Surveys, 61:2 (2006), 365–367  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. S. P. Suetin, “Trace formulae for a class of Jacobi operators”, Sb. Math., 198:6 (2007), 857–885  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Baratchart, L, “Multipoint Pade approximants to complex Cauchy transforms with polar singularities”, Journal of Approximation Theory, 156:2 (2009), 187  crossref  mathscinet  zmath  isi  scopus  scopus
    11. S. P. Suetin, “Numerical Analysis of Some Characteristics of the Limit Cycle of the Free van der Pol Equation”, Proc. Steklov Inst. Math., 278, suppl. 1 (2012), S1–S54  mathnet  crossref  crossref  isi  elib
    12. Derevyagin M., Derkach V., “Convergence of Diagonal Pade Approximants for a Class of Definitizable Functions”, Recent Advances in Operator Theory in Hilbert and Krein Spaces, Operator Theory Advances and Applications, 198, 2010, 97–124  mathscinet  zmath  isi
    13. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. A. V. Komlov, S. P. Suetin, “An asymptotic formula for polynomials orthonormal with respect to a varying weight”, Trans. Moscow Math. Soc., 73 (2012), 139–159  mathnet  crossref  mathscinet  zmath  elib
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