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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 11 scientific papers (total in 11 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 (11)
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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 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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