Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research the Institute Computer Science, Czestochowa University Technology

Let G and $$\Omega $$ be two planar domains. We give necessary sufficient conditions on a sequence $$(\phi _n)$$ of eventually injective holomorphic mappings from to for the existence function $$f\in H(\Omega )$$ whose orbit under composition by is dense in H(G). This extends result same nature obtained Grosse-Erdmann Mortini when $$G=\Omega . An interconnexion between topological properties ap...

A complex scalar ? is said to be an extended eigenvalue of a bounded linear operator on Hilbert space if there nonzero X such that AX=?XA. The results in this paper provide full solution the problem computing eigenvalues for those composition operators C? induced Hardy H2(D) by fractional transformations ? unit disk.

In this paper we study the boundedness of composition operators on weighted Bergman spaces and Hardy space over polydisc Dn. Studying volume sublevel sets show for which n necessary conditions obtained by Bayart are sufficient. For arbitrary prove rank sufficiency theorem which, in particular, provides us with a simple criterion describing bidisc. Such consistent characterization is classical t...