We present a conjecture that the asymptotics for Chebyshev polynomials in a complex domain can be given in terms of the reproducing kernels of a suitable Hilbert space of analytic functions in this domain. It is based on two classical results due to Garabedian and Widom. To support this conjecture we study the asymptotics for Ahlfors extremal polynomials in the complement to a system of intervals on R, arcs on T, and the asymptotics of the extremal entire functions for the continuous counterpart of this problem. Bibliography: 35 titles.
Bibliographical notePublisher Copyright:
© 2018 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.
- Abel-Jacobi inversion
- Chebyshev polynomial
- analytic capacity
- complex Greens and Martin functions
- hyperelliptic Riemann surface
- reproducing kernel.