Article
Licensed
Unlicensed
Requires Authentication
Analytic in planar domains functions with preassigned asymptotic set
-
Ekaterina G. Ganenkova
and
Victor V. Starkov
Published/Copyright:
May 1, 2014
Abstract.
In 1954 M. Heins proved that, for every analytic set A containing the infinity, there exists an entire function whose set of asymptotic values at the infinity equals A. We obtain analogs of this result for functions analytic in planar domains of arbitrary connectivity.
Keywords: Asymptotic value; analytic set
MSC: 30C40
Funding source: Programm of Strategic Development of the PetrSU
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: N 14-01-00510
Funding source: Ministry of Education and Science of the Russian Federation
Award Identifier / Grant number: No 2014/154, NIR No 191
The authors would like to thank S. Y. Graf for his participation in discussions and sharing his knowledge.
Received: 2013-10-21
Revised: 2014-3-20
Accepted: 2014-3-28
Published Online: 2014-5-1
Published in Print: 2014-6-1
© 2014 by Walter de Gruyter Berlin/Boston
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Frontmatter
- Porosity and the bounded linear regularity property
- Analytic in planar domains functions with preassigned asymptotic set
- Multiplication of the distributions (x±i0)z
- Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
- Modes of ideal continuity and the additive property in the Riesz space setting
- On complex Fermi curves of two-dimensional, periodic Schrödinger operators
- On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter
- On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev–Ibragimov operators
- On series whose rearrangements possess discrete sets of limit points
- A system of two conservation laws with flux conditions and small viscosity
Articles in the same Issue
- Frontmatter
- Porosity and the bounded linear regularity property
- Analytic in planar domains functions with preassigned asymptotic set
- Multiplication of the distributions (x±i0)z
- Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle
- Modes of ideal continuity and the additive property in the Riesz space setting
- On complex Fermi curves of two-dimensional, periodic Schrödinger operators
- On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter
- On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev–Ibragimov operators
- On series whose rearrangements possess discrete sets of limit points
- A system of two conservation laws with flux conditions and small viscosity
