Approximation by Generalized Faber Series in Weighted Bergman Spaces on Infinite Domains With a Quasiconformal Boundary
DOI:
https://doi.org/10.5644/SJM.02.1.03Keywords:
Weighted Bergman spaces, quasiconformal curves, Faber seriesAbstract
Using an integral representation on infinite domains with a quasiconformal boundary the generalized Faber series for the functions in the weighted Bergman space $A^{2}(G,\omega )$ are defined and its approximation properties are investigated.
2000 Mathematics Subject Classification. 30E10, 41A10, 41A25, 41A58
Downloads
References
L. Ahlfors, Lectures on Quasiconformal Mapping, Wadsworth, Belmont, CA, 1987.
V. V. Andrievski, V. I. Belyi and V. K. Dzyadyk, Conformal Invariants in constructive Theory of Functions of Complex Variable, Adv. Series in Math. Sciences and Engineer., WEP Co., Atlanta, Georgia, 1995.
I. M. Batchaev, Integral Representations in a Region with Quasiconformal Boundary and Some Applications, Doctoral dissertation, Baku, 1980.
V. I. Belyi, Conformal mappings and approximation of analytic functions in domains with quasiconformal boundary, USSR-Sb. 31 (1997), 289–317.
A. Cavus, Approximation by generalized Faber series in Bergman spaces on finite regions with a qusiconformal boundary, J. Approx. Theory, 87 (1996), 25–35.
R. A. De Vore, G. G. Lorentz, Constructive Approximation, Spriger-Verlag, New York/Berlin, 1993.
D. Gaier, Lectures on Complex Approximation, Birkh¨auser, Boston/Basel/Stutgart, 1987.
D. M. Israfilov, Approximation by generalized Faber series in weighted Bergman spaces on finite domains with quasiconformal boundary, East Journal on Approx., 4 (1998), 1–13.
D. M. Israfilov, Approximative properties of generalized Faber series, In: Proc. AllUnion Scholl on Approximative Theory, Baku, May, 1989.
D. M. Israfilov, Faber series in weighted Bergman spaces, Complex Variables, 45 (2001), 167–181.
O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, Springer-Verlag, New York/Berlin, 1973.
P. K. Suetin, Series of Faber Polynomials, Gordon and Breach Science Publishers, Amsterdam, 1998.
