On the transmutation of the Lions operator to the simplest form

TitleOn the transmutation of the Lions operator to the simplest form
Publication TypeJournal Article
Year of Publication2017
AuthorsLinchuk, Yu.S
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published3/2017
Let $\alpha \in \mathbb{C}, m \in N, m \geqslant 2$, and $L_{\alpha } = \frac{d^{m}}{dz^{m}} + \frac{\alpha }{z}\frac{d^{m-1}}{dz^{m-1}}$. We investigate the conditions of equivalence of the Lions operator  $L_{\alpha }$ 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.
Keywordschaotic operator, equivalent operators, hypercyclic operator, Lions operator, spaces of analytic functions, transmutation operators
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