Geodesic
Hypercyclicity and Chaotic Character of Generalized Convolution Operators Generated by Gelfond--Leontev Operators
Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 849-856

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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
Mots-clés : Fréchet space. 
@article{MZM_2009_85_6_a4,
     author = {V. E. Kim},
     title = {Hypercyclicity and {Chaotic} {Character} of {Generalized} {Convolution} {Operators} {Generated} by {Gelfond--Leontev} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {849--856},
     publisher = {mathdoc},
     volume = {85},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a4/}
}
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V. E. Kim. Hypercyclicity and Chaotic Character of Generalized Convolution Operators Generated by Gelfond--Leontev Operators. Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 849-856. http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a4/