On the transmutation of the Lions operator to the simplest form

1Linchuk, Yu.S
1Yuriy Fedkovych Chernivtsi National University
Dopov. Nac. akad. nauk Ukr. 2017, 3:8-13
https://doi.org/10.15407/dopovidi2017.03.008
Section: Mathematics
Language: Ukrainian
Abstract: 
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.
Keywords: chaotic operator, equivalent operators, hypercyclic operator, Lions operator, spaces of analytic functions, transmutation operators
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