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Dynamic Approach

  • David Shoikhet
  • Mark Elin
Chapter
  • 585 Downloads
Part of the Operator Theory: Advances and Applications book series (OT, volume 208)

Abstract

Dynamic approach to the study of starlike and spirallike functions is based on the following observation. Let ƒ ∈ Univ(Δ), then ƒ is spirallike if and only if there is μ ∈ C with Reμ > 0 such that
$$ e^{ - \mu t} f(\Delta ) \subset \Delta $$
for all t ≥ 0. Then, for each t ≥ 0, the function
$$ F_t (z) = f^{ - 1} (e^{ - \mu t} f(z)) $$
(2.0.1)
is a well-defined holomorphic self-mapping of the open unit disk Δ.

Keywords

Cauchy Problem Holomorphic Function Boundary Point Univalent Function Dynamic Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • David Shoikhet
    • 1
  • Mark Elin
    • 1
  1. 1.Department of MathematicsORT Braude CollegeKarmielIsrael

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