Applications of Jentzsch-Szegő and Erdős-Turán Type Theorems
Chapter
Abstract
In this chapter we consider applications of Jentzsch-Szegő type and Erdős-Turán type theorems that were derived in Chapter 2.
Keywords
Orthogonal Polynomial Limit Point Jordan Curve Type Theorem Equilibrium Measure
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
Historical Comments
- [180]J.L. Walsh (1959): The analogue for maximally convergent polynomials of Jentzsch’s theorem. Duke Math. J., 26: 605–616.Google Scholar
- [59]M. Fekete, J.L. Walsh (1955): On the asymptotic behaviour of polynomials with extremal properties, and of their zeros. J. Anal. Math., 4: 49–87.Google Scholar
- [41]P. Borwein (1984): The relationship between the zeros of best approximation and differentiability. Proc. Amer. Math. Soc., 92: 528–532.Google Scholar
- [38]H.-P. Blatt, E.B. Saff, M. Simkani (1988): Jentzsch-Szegd type theorems for the zeros of best approximants. J. London Math. Soc., 38: 307–316.Google Scholar
- [88]K.G. Ivanov, E.B. Saff, V. Totik (1991): On the behavior of zeros of polynomials of best and near-best approximations. Canad. J. Math., 43: 10101021.Google Scholar
- [80]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.CrossRefGoogle Scholar
- [155]E.B. Saff, V. Totik (1989): Behavior of polynomials of best uniform approximation. Trans. Amer. Math. Soc., 316: 567–593.Google Scholar
- [20]V.V. Andrievskii, H.-P. Blatt (1999): Erdfis-Turdn Type Theorems on Quasiconformal Curves and Arcs. J. Approx. Theory, 97: 334–365.Google Scholar
- [31]H.-P. Blatt, R. Grothmann (1991): Erdös-Turcin theorems on a system of Jordan curves and arcs. Constr. Approx., 7: 19–47.Google Scholar
- [79]R. Grothmann (1996): Distribution of interpolation points. Ark. Mat., 34: 103–117.Google Scholar
Copyright information
© Springer Science+Business Media New York 2002