A note on the Königs domain of compact composition operators on the Bloch space
Jones, Matthew (2011) A note on the Königs domain of compact composition operators on the Bloch space. Journal of Inequalities and Applications (31). ISSN 1029-242X
Let D be the unit disk in the complex plane. We define B0 to be the little Bloch space of functions f analytic in D which satisfy lim┬(|z|→1)〖(1- |z|^2 )|f^' (z) |=0.〗 If φ:D→D is analytic then the composition operator C_φ:f→f∘φ is a continuous operator that maps B0 into itself. In this paper, we show that the compactness of C_φ, as and operator on B0, can be modelled geometrically by its principle eigenfunction. In particular, under certain necessary conditions, we relate the compactness of C_φto the geometry of Ω=σ(D) where σ satisfies Schroder’s functional equation σ∘φ=φ^' (0)σ.
|Research Areas:||A. > School of Science and Technology > Design Engineering and Mathematics|
|Depositing User:||Devika Mohan|
|Date Deposited:||26 Sep 2011 07:32|
|Last Modified:||10 May 2015 16:44|
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