Dynamic Approach

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


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
$$ F_t (z) = f^{ - 1} (e^{ - \mu t} f(z)) $$
is a well-defined holomorphic self-mapping of the open unit disk Δ.


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

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

Personalised recommendations