Abstract
We obtain the conditions for the similarity of the generalized Bessel operator of m-th order to the operator of m-fold differentiation in the space of all m-even analytic functions in arbitrary domains. We investigate some properties of diagonal operators in this space. We also describe the commutant of the generalized Bessel operator. We investigate the hypercyclicity for the elements of the commutant of the generalized Bessel operator.
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