# On the transmutation of the Lions operator to the simplest form

 1Linchuk, Yu.S1Yuriy 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
References:
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