Abstract:
We consider generalized convolution operators generated by operators of Gelfond–Leontev generalized differentiation. In this paper, we prove that any such operator not coinciding with the operator of multiplication by a constant is hypercyclic and chaotic on the space of all entire functions. This result generalizes earlier results belonging to the classical convolution operators as well as to the generalized convolution operators constructed by using Dunkl operators.
Citation:
V. E. Kim, “Hypercyclicity and Chaotic Character of Generalized Convolution Operators Generated by Gelfond–Leontev Operators”, Mat. Zametki, 85:6 (2009), 849–856; Math. Notes, 85:6 (2009), 807–813
This publication is cited in the following 12 articles:
A. I. Rakhimova, “Hypercyclic and chaotic operators in space of functions analytic in domain”, Ufa Math. J., 16:3 (2024), 84–91
A. V. Bratishchev, “On Gelfond–Leontiev Operators of Generalized Differentiation”, J. Math. Sci. (N. Y.), 252:3 (2021), 319–344
Ben Hammouda M.S., Bennasr L., Fitouhi A., “on Harmonic Analysis Associated With the Hyper-Bessel Operator of the Complex Plane”, J. Inequal. Spec. Funct., 8:1, SI (2017), 118–129
Bernal-Gonzalez L., Bonilla A., “Rate of Growth of Hypercyclic and Frequently Hypercyclic Functions for the Dunkl Operator”, Mediterr. J. Math., 13:5 (2016), 3359–3372
Med Saber Ben Hammouda, “RETRACTED ARTICLE: Convolution Operators Associated with the Generalized Airy Operator on the Complex Plane”, Complex Anal. Oper. Theory, 10:1 (2016), 231
L. Bennasr, “Dynamics of the basic Bessel operator and related convolution operators on spaces of entire functions”, Complex Anal. Oper. Theory, 9:1 (2015), 167–181
I. I. Karamov, V. V. Napalkov, “Generalized Dunkl operator”, Ufa Math. J., 6:1 (2014), 56–65
V. E. Kim, “Dynamics of linear operators connected with su(1,1) algebra”, Ufa Math. J., 6:1 (2014), 66–70
L. Bennasr, M. S. Ben Hammouda, A. Fitouhi, “On linear dynamics in quantum calculus”, Results Math., 65:3-4 (2014), 415–428
V. E. Kim, “Sobstvennye funktsii operatorov unichtozheniya, assotsiirovannykh s kommutatsionnymi sootnosheniyami Vignera”, Ufimsk. matem. zhurn., 4:1 (2012), 82–87
Kim V.E., “Commutation relations and hypercyclic operators”, Arch. Math. (Basel), 99:3 (2012), 247–253
V. E. Kim, “Polnota sistem proizvodnykh funktsii Eiri i gipertsiklicheskie operatory”, Ufimsk. matem. zhurn., 2:4 (2010), 52–57