Published January 1, 2017
| Version v1
Journal article
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A Description Method in the Value Region Problem
Creators
- 1. Saratov NG Chernyshevskii State Univ, Dept Math & Mech, Saratov 410012, Russia
Description
Fedorov completely described the value region , , over the class of holomorphic univalent functions in the unit disk with real coefficients , . We extend this result to the class of bounded functions satisfying in . The problem is formulated as the reachable set problem for the Hamilton system of controllable differential equations in the frames of the Loewner theory. A family of Cauchy problems is substituted for the family of boundary value problems. The free parameter in the initial data serves as a parameter for the boundary curve of the value region. The algorithm proposed can be useful in other similar value region problems.
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