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Matematicheskie Zametki, 2009, Volume 85, Issue 6, Pages 849–856
DOI: https://doi.org/10.4213/mzm4427 (Mi mzm4427) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Hypercyclicity and Chaotic Character of Generalized Convolution Operators Generated by Gelfond–Leontev Operators

V. E. Kim

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Full-text PDF (460 kB) Citations (12)
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DOI: https://doi.org/10.4213/mzm4427
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.
Keywords: generalized convolution operator, Gelfond–Leontev generalized differentiation, Dunkl operator, topological vector space, generalized Laplace transform, Fréchet space.
Received: 15.01.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 6, Pages 807–813
DOI: https://doi.org/10.1134/S000143460905023X
Bibliographic databases:
UDC: 517.983+517.53
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    1. A. I. Rakhimova, “Hypercyclic and chaotic operators in space of functions analytic in domain”, Ufa Math. J., 16:3 (2024), 84–91  mathnet  crossref
    2. A. V. Bratishchev, “On Gelfond–Leontiev Operators of Generalized Differentiation”, J. Math. Sci. (N. Y.), 252:3 (2021), 319–344  mathnet  mathnet  crossref
    3. 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  mathscinet  isi
    4. 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  crossref  mathscinet  zmath  isi  scopus
    5. 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  crossref
    6. 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  crossref  mathscinet  zmath  isi  scopus
    7. I. I. Karamov, V. V. Napalkov, “Generalized Dunkl operator”, Ufa Math. J., 6:1 (2014), 56–65  mathnet  crossref  isi  elib
    8. V. E. Kim, “Dynamics of linear operators connected with $\mathrm{su}(1,1)$ algebra”, Ufa Math. J., 6:1 (2014), 66–70  mathnet  crossref  elib
    9. L. Bennasr, M. S. Ben Hammouda, A. Fitouhi, “On linear dynamics in quantum calculus”, Results Math., 65:3-4 (2014), 415–428  crossref  mathscinet  zmath  isi  scopus
    10. V. E. Kim, “Sobstvennye funktsii operatorov unichtozheniya, assotsiirovannykh s kommutatsionnymi sootnosheniyami Vignera”, Ufimsk. matem. zhurn., 4:1 (2012), 82–87  mathnet
    11. Kim V.E., “Commutation relations and hypercyclic operators”, Arch. Math. (Basel), 99:3 (2012), 247–253  crossref  mathscinet  zmath  isi  scopus
    12. V. E. Kim, “Polnota sistem proizvodnykh funktsii Eiri i gipertsiklicheskie operatory”, Ufimsk. matem. zhurn., 2:4 (2010), 52–57  mathnet  zmath  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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