Orthogonal polynomials with complex-valued weight function, I

Springer Science and Business Media LLC - Tập 2 Số 1 - Trang 225-240 - 1986
Herbert Stahl1
1TU-Berlin/Sekr. FR 6-8, Berlin 10, Fed. Rep. Germany

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H. Hamburger (1920/21):Über eine Erweiterung des Stieltjesschen Momentenproblems, Teil I, II und III. Math. Ann.,81:235–319, Math. Ann.,82:120–164, 168–187.

G. Szegö (1967): Orthogonal Polynomials, 3rd ed. Providence, RI: American Mathematical Society.

G. Baxter (1971):A convergence equivalence related to polynomials orthogonal on the unit circle, Trans. Amer. Math. Soc.,79:471–487.

J. Nuttall (1972): Orthogonal Polynomials for Complex Weight Functions and the Convergence of Related Padé Approximants. (Private communication.)

H. Stahl (1974): Orthogonal Polynomials of Complex-valued Measures and the convergence of Padé Approximants, Coll. Math. Soc. Janos Bolyai, 19. Budapest: Fourier Analysis and Approximation Theory.

H. Stahl (1985):Extremal domains associated with an analytic function I, II, Complex Variables4:311–324, 325–338.

T. Bagby (1967):The modulus of a plane condenser, J. Math. Mech.17:315–329.

N. S. Landk of (1972): Foundation of Modern Potential Theory. Berlin: Springer-Verlag.

H. Stahl (1985):Structure of extremal domains associated with an analytic function. Complex Variables4:339–354.

R. Courant (1950): Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces. New York: Springer-Verlag.

Ch. Pommerenke (1959):On the derivative of a polynomial. Michigan Math. J.,6:373–375.

J. Nuttall (1977):The convergence of Padé approximants to functions with branch points, In: Padé and Rational Approximation (E. B. Saff and R. S. Varga, eds.). New York: Academic Press.

J. Nuttall, S. R. Singh (1977):Orthogonal polynomials and Padé approximants associated with a system of Arcs. J. Approx. Theory,21:1–42.

A. Magnus (to appear):Toeplitz matrix techniques and convergence of complex weight Padé approximants. New York: Springer-Verlag.

A. A. Gonchar, G. Lopez (1978):On Markov's theorem for multipoint Padé approximants, Mat. Sb., 105(147),4:512–527. English translation in Math. U.S.S.R. Sb.,34 (1978).