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P. Túrán (1975)
On orthogonal polynomialsAnalysis Mathematica, 1
C. Pommerenke (1992)
Boundary Behaviour of Conformal Maps
R. Lehman (1957)
Development of the mapping function at an analytic corner.Pacific Journal of Mathematics, 7
G. Julia (1932)
Sur la représentation conforme des aires triplement connexesCommentarii Mathematici Helvetici, 4
V. Andrievskii, I. Pritsker (2000)
Convergence of Bieberbach polynomials in domains with interior cuspsJournal d’Analyse Mathématique, 82
V. Smirnov, N. Lebedev (1968)
Functions of a complex variable : constructive theory
P. Duren (1970)
Theory of H[p] spaces
V. Andrievskii, V. Belyi, Vladislav Dzi︠a︡dyk (1995)
Conformal invariants in constructive theory of functions of complex variable
D. Gaier (1988)
On the convergence of the Bieberbach polynomials in regions with cornersConstructive Approximation, 4
(1939)
Sur l'approximation en moyenne quadratique des fonctions analytiques
D. Gaier, R. Mclaughlin (1987)
Lectures on complex approximation
Pritsker E-mail: igor@math.okstate.edu Address: Department of Mathematics, 401 Mathematical Sciences
V. Andrievskii (1983)
Convergence of Bieberbach polynomials in domains with quasiformal boundaryUkrainian Mathematical Journal, 35
D. Gaier (1992)
On the convergence of the Bieberbach polynomials in regions with piecewise analytic boundaryArchiv der Mathematik, 58
L. Bieberbach (1914)
Zur theorie und praxis der konformen abbildungRendiconti del Circolo Matematico di Palermo (1884-1940), 38
R. Stephenson (1962)
A and VBritish Journal of Ophthalmology, 46
P. Suetin (1966)
FUNDAMENTAL PROPERTIES OF POLYNOMIALS ORTHOGONAL ON A CONTOURRussian Mathematical Surveys, 21
Keldysch, Lavrentieff (1937)
Sur la représentation conforme des domaines limites par des courbes rectifiablesAnnales Scientifiques De L Ecole Normale Superieure, 54
J. Clarkson, P. Erdös (1943)
Approximation by polynomialsDuke Mathematical Journal, 10
D. Gaier (1998)
Polynomial Approximation of Conformal MapsConstructive Approximation, 14
(1956)
Recent results in numerical methods of conformal mapping
D. Gaier (1964)
Konstruktive Methoden der konformen AbbildungMathematics of Computation, 19
V V Andrievskii, D Gaier (1992)
Uniform convergence of Bieberbach polynomials in domains with piecewise quasianalytic boundaryMitt. Math. Sem. Giessen, 211
P C Rosenbloom, S E Warschawski (1955)
Approximation by polynomialsLectures on Functions of a Complex Variable
P K Suetin (1966)
Fundamental properties of polynomials orthogonal on a contourUspekhi Mat. Nauk, 21
Keldysh , On a class of extremal polynomials ,
M V Keldysh (1936)
On a class of extremal polynomialsDokl. Akad. Nauk SSSR, 4
G. Julia, G. Bourion, J. Leray (1934)
Leçons sur la représentation conforme des aires multiplement connexes
We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed through the smallest exterior angle at the boundary. Furthermore, we show that the rate of approximation on compact subsets inside the domain is essentially the square of that on the closure. Two standard applications to the rate of decay for the contour orthogonal polynomials inside the domain, and to the rate of locally uniform convergence of Fourier series are also given.
Computational Methods and Function Theory – Springer Journals
Published: Mar 1, 2004
Keywords: Conformal mapping; Szegő kernel; Fourier series; orthogonal polynomials; 30C40; 30E10; 41A10; 30C30
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