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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
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