Zeros and local extreme points of Faber polynomials associated with hypocycloidal domains. (English) Zbl 0815.30008
Faber polynomials play an important role in different 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.
Reviewer: M.Eiermann
MSC:
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
