Michael Eiermann and Richard S. Varga, Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains, ETNA (Electronic Transactions on Numerical Analysis) 1(1993), 49-71. MR 94i:30006. Zbl. 815.30008.

Abstract. Faber polynomials play an important role in di erent areas of constructive complex analysis. Here, the zeros and local extreme points of Faber polynomials for hypocycloidal domains are studied. For this task, we use tools from linear algebra, namely, the Perron-Frobenius theory of nonnegative matrices, the Gantmacher-Krein theory of oscillation matrices, and the Schmidt-Spitzer theory for the asymptotic spectral behavior of banded Toeplitz matrices.


full paper