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Generalization of results about the Bohr radius for power series

100%

Aizenberg L.

Studia Mathematica

2007

tom 180

nr 2

161-168

The Bohr radius for power series of holomorphic functions mapping Reinhardt domains 𝓓 ⊂ ℂⁿ into a convex domain G ⊂ ℂ is independent of the domain G.

On the Rogosinski radius for holomorphic mappings and some of its applications

51%

Aizenberg L., Elin M., Shoikhet D.

Studia Mathematica

2005

tom 168

nr 2

147-158

The well known theorem of Rogosinski asserts that if the modulus of the sum of a power series is less than 1 in the open unit disk: $|∑_{n=0}^{∞} aₙzⁿ| < 1$, |z| < 1, then all its partial sums are less than 1 in the disk of radius 1/2: $|∑_{n=0}^{k} aₙzⁿ| < 1$, |z| < 1/2, and this radius is sharp. We present a generalization of this theorem to holomorphic mappings of the open unit ball into an arbitrary convex domain. Other multidimensional analogs of Rogosinski's theorem as well as some applications to dynamical systems are considered.

Ograniczanie wyników

2 Studia Mathematica

2 Aizenberg L.

1 Elin M.

1 Shoikhet D.

1 2007

1 2005

Wyniki wyszukiwania

Generalization of results about the Bohr radius for power series

On the Rogosinski radius for holomorphic mappings and some of its applications