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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 961209, 21 pages
On the Distribution of Zeros and Poles of Rational Approximants on Intervals
1Department of Mathematical Sciences, Kent State University, Kent, OH 44242-0001, USA
2Lehrstuhl für Mathematik-Angewandte Mathematik, Mathematisch-Geographische Fakulätt, Katholische Universität Eichstätt-Ingolstadt, 85071 Eichstätt, Germany
3Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Received 29 February 2012; Accepted 8 May 2012
Academic Editor: Karl Joachim Wirths
Copyright © 2012 V. V. Andrievskii et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. A. Gončar, “On the convergence of generalized Padé approximants of meromorphic functions,” Matematicheskii Sbornik, vol. 98(140), no. 4(12), pp. 564–577, 1975, English translation in Mathematics of the USSR-Sbornik, vol. 27, no. 4, pp. 503–514, 1975.
- H.-P. Blatt, R. Grothmann, and R. K. Kovacheva, “Regions of meromorphy and value distribution of geometrically converging rational functions,” Journal of Mathematical Analysis and Applications, vol. 382, no. 1, pp. 66–76, 2011.
- H.-P. Blatt and R. K. Kovacheva, “Growth behavior and zero distribution of rational approximants,” Constructive Approximation, vol. 34, no. 3, pp. 393–420, 2011.
- H.-P. Blatt and E. B. Saff, “Behavior of zeros of polynomials of near best approximation,” Journal of Approximation Theory, vol. 46, no. 4, pp. 323–344, 1986.
- H.-P. Blatt, E. B. Saff, and M. Simkani, “Jentzsch-Szegö type theorems for the zeros of best approximants,” Journal of the London Mathematical Society, vol. s2-38, no. 2, pp. 307–316, 1988.
- H. Stahl, “Poles and zeros of best rational approximants of ,” Constructive Approximation, vol. 10, no. 4, pp. 469–522, 1994.
- E. B. Saff and H. Stahl, “Ray sequences of best rational approximants for ,” Canadian Journal of Mathematics, vol. 49, no. 5, pp. 1034–1065, 1997.
- H.-P. Blatt and G. G. Lorentz, “On a Theorem of Kadec,” in Proceedings of the Conference on Constructive Theory of Functions, Varna, 1987, Sedov, Petrushev, Moleev, and Tashev, Eds., pp. 56–64, Bulgarian Academy of Sciences, 1988.
- M. I. Kadec, “On the distribution of points of maximum deviation in the approximation of continuous functions by polynomials,” Uspekhi Matematicheskikh Nauk, vol. 15, no. 1(91), pp. 199–202, 1960.
- H.-P. Blatt, “The interaction of alternation points and poles in rational approximation,” Journal of Computational and Applied Mathematics, vol. 179, no. 1-2, pp. 31–46, 2005.
- H.-P. Blatt, R. Grothmann, and R. K. Kovacheva, “Poles and alternation points in real rational Chebyshev approximation,” Computational Methods and Function Theory, vol. 3, no. 1, pp. 165–177, 2003.
- P. B. Borwein, A. Kroó, R. Grothmann, and E. B. Saff, “The density of alternation points in rational approximation,” Proceedings of the American Mathematical Society, vol. 105, no. 4, pp. 881–888, 1989.
- D. Braess, D. S. Lubinsky, and E. B. Saff, “Behavior of alternation points in best rational approximation,” Acta Applicandae Mathematicae, vol. 33, no. 2-3, pp. 195–210, 1993.
- A. Kroó and F. Peherstorfer, “On the asymptotic distribution of oscillation points in rational approximation,” Analysis Mathematica, vol. 19, no. 3, pp. 225–232, 1993.
- A. A. Gončar, “Properties of functions related to their rate of approximability by rational functions,” American Mathematical Society Translations Series 2, vol. 91, pp. 99–127, 1970.
- D. J. Newman, “Rational approximation to ,” The Michigan Mathematical Journal, vol. 11, pp. 11–14, 1964.
- G. Meinardus, Approximation of Functions: Theory and Numerical Methods, Springer, New York, NY, USA, 1967.
- P. Erdős and P. Turán, “On the distribution of roots of polynomials,” Annals of Mathematics, vol. 51, pp. 105–119, 1950.
- V. V. Andrievskii and H.-P. Blatt, Discrepancy of Signed Measures and Polynomial Approximation, Springer, New York, NY, USA, 2002.
- A. A. Gončar, “A local condition of single-valuedness of analytic functions,” Mathematics of the USSR-Sbornik, vol. 18, no. 1, pp. 148–164, 1972.
- J. L. Walsh, “Overconvergence, degree of convergence, and zeros of sequences of analytic functions,” Duke Mathematical Journal, vol. 13, pp. 195–234, 1946.