Computational Methods and Function Theory 2 (2002), No. 2, 353--366
Copyright Heldermann Verlag 2002
Mark Elin
elin_mark@hotmail.com, Department of Mathematics, Braude College, 21982 Karmiel, Israel.
Victor Goryainov
goryainov_vv@hotmail.com, Department of Economics and Mathematics, Volzhsky Institute of Humanities of Volgograd State University, 404133 Volzhsky, Russia.
Simeon Reich
sreich@tx.technion.ac.il, Department of Mathematics, The Technion --- Israel Institute of Technology, 32000 Haifa, Israel.
David Shoikhet
davs@tx.technion.ac.il, Department of Mathematics, Braude College, 21982 Karmiel, Israel.
We establish criteria for the embeddability of an analytic function into a semigroup of analytic self-mappings of the open unit disk. We do this by studying properties of solutions to the Abel and Schr\"oder functional equations.
Keywords: Embeddability, fractional iteration, functional equation, infinitesimal generator, Koenigs function, semigroup of analytic functions.
MSC 2000: 30D05, 39B12, 39B32.
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