On the convergence of Padé approximations for generalized Nevanlinna functions
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M. S. Derevyagin and V. A. Derkach
Translated by: O. A. Khleborodova - Trans. Moscow Math. Soc. 2007, 119-162
- DOI: https://doi.org/10.1090/S0077-1554-07-00163-X
- Published electronically: October 29, 2007
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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.References
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Bibliographic 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
- Published electronically: October 29, 2007
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2007, 119-162
- MSC (2000): Primary 30E05; Secondary 47A57
- DOI: https://doi.org/10.1090/S0077-1554-07-00163-X
- MathSciNet review: 2429269