Presents some important classical and modern results of the series of Faber polynomials and their applications. Interest in this subject has increased rapidly over the last decade, although the presentation of research has, until now, been confined mainly to journal articles. Applications include theory of functions of complex variables, theory of analytic function approximation, and some aspects of numerical analysis.
1. Some Results of Approximation Theory 2. The Elementary Properties of Faber Polynomials 3. Asymptotic Properties of Faber Polynomials 4. Convergence of Faber Series Inside a Domain 5. Series of Faber Polynomials 6. Some Properties of Faber Operators 7. Faber Series in a Closed Domain 8. Faber Polynomials and the Theory of Univalent Functions 9. Faber Series and the Riemann Boundary Problem 10. Generalization of Faber 11. Polynomials and Series 12. Some Recent Results 13. Faber Series with the Simplest Conditions 14. The Summation Formula of Dzyadyk 15. Faber Series in Canonical Domains