On the transmutation of the Lions operator to the simplest form
DOI:
https://doi.org/10.15407/dopovidi2017.03.008Keywords:
chaotic operator, equivalent operators, hypercyclic operator, Lions operator, spaces of analytic functions, transmutation operatorsAbstract
Let α∈C,m∈N,m⩾2, and Lα=dmdzm+αzdm−1dzm−1. We investigate the conditions of equivalence of the Lions operator Lα to simpler operators in subspaces of the spaces of functions analytic in domains. We establish the hypercyclicity and the chaoticity of a class of operators.
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