Abstract
In this chapter we consider the approximation of a piecewise analytic function on touching domains by polynomials and the convergence of Bieberbach polynomials in domains with quasiconformal boundary. We have already used some of the results of this chapter in previous sections.
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Historical Comments
V.V. Andrievskii (1996): Polynomial approximation to a piecewise analytic function on touching domains. Complex Variables, 31: 325–344.
R. Grothmann, E.B. Saff (1988): On the behavior of zeros and poles of best uniform polynomial and rational approximants. Nonlinear numerical methods and rational approximation (ed. A. Cuyt), Reidel, Dordrecht: 57–75.
J.M. Anderson, W.H.J. Fuchs (1988): Remarks on “almost best” approximation in the complex plane. Complex Analysis (ed. J. Hersch, A. Huber ): 17–25.
E.B. Saff, V. Totik (1989): Polynomial approximation of piecewise analytic functions. J. London Math. Soc., 39: 487–498.
D. Gaier (1997): Complex approximation on touching domains. Complex Variables, 34: 325–342.
M.V. Keldysh (1939): Sur l’approximation en moyenne quadratique des fonctions analytiques. Mat. Sb., 5: 391–401.
S.N. Mergelyan (1951): Some questions in constructive function theory. Tr. Mat. Inst. Steklova, Akad. Nauk SSSR, 37: 3–91 (Russian).
Wu Xue-Mou (1963): On Bieberbach polynomials. Acta Math. Sinica, 13: 145–151.
P.K. Suetin (1971): Polynomials orthogonal over a region and Bieberbach polynomials. Proc. Steklov Inst. Math., 100. Providence, RI 1974. American Math. Society.
I.B. Simonenko (1978): Convergence of Bieberbach polynomials in the case of a Lipschitz domain. Math USSR-Izv., 13: 166–174.
V.V. Andrievskii (1984): Convergence of Bieberbach polynomials in domains with quasiconformal boundary. Ukrainian Math J., 32: 435–440 (Russian).
D. Gaier (1987): On a polynomial lemma of Andrievskii. Arch. Math., 49: 119–123.
D. Gaier (1988): On the convergence of Bieberbach polynomials in regions with corners. Constr. Approx., 4: 289–305.
D. Gaier (1992): On the convergence of Bieberbach polynomials in regions with piecewise analytic boundary. Arch. Math., 58: 462–470.
V.V. Andrievskii, D. Gaier (1992): Uniform convergence of Bieberbach polynomials in domains with piecewise quasianalytic boundary. Mitt. Math. Sem. Giessen, 211: 49–60.
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© 2002 Springer Science+Business Media New York
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Andrievskii, V.V., Blatt, HP. (2002). Special Topics. In: Discrepancy of Signed Measures and Polynomial Approximation. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4999-1_8
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DOI: https://doi.org/10.1007/978-1-4757-4999-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3146-7
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