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Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

On the convergence of Padé approximations for generalized Nevanlinna functions


Authors: M. S. Derevyagin and V. A. Derkach
Translated by: O. A. Khleborodova
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 68 (2007).
Journal: Trans. Moscow Math. Soc. 2007, 119-162
MSC (2000): Primary 30E05; Secondary 47A57
Posted: October 29, 2007
MathSciNet review: 2429269
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Abstract: We study a stepwise algorithm for solving the indefinite truncated moment problem and obtain the factorization of the matrix describing the solution of this problem into elementary factors. We consider the generalized Jacobi matrix corresponding to Magnus' continuous $ P$-fraction that appears in this algorithm and the polynomials of the first and second kind that are solutions of the corresponding difference equation. Weyl functions and the resolution matrices for finite and infinite Jacobi matrices are computed in terms of these polynomials. Convergence of diagonal and paradiagonal Padé approximation for functions from the generalized Nevanlinna class is studied.


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Additional Information

M. S. Derevyagin
Affiliation: Donetsk National University, Universitetskaya 24, 83055 Donetsk, Ukraine
Email: derkach.v@gmail.com

V. A. Derkach
Affiliation: Donetsk National University, Universitetskaya 24, 83055 Donetsk, Ukraine
Email: derevyagin.m@gmail.com

DOI: http://dx.doi.org/10.1090/S0077-1554-07-00163-X
PII: S 0077-1554(07)00163-X
Posted: October 29, 2007
Article copyright: © Copyright 2007 American Mathematical Society