Abstract:
We study hypercyclicity properties of a family of non-convolution operators defined on the spaces of entire functions on CN. These operators are a composition of a differentiation operator and an affine composition operator, and are analogues of operators studied by Aron and Markose on H(C). The hypercyclic behavior is more involved than in the one dimensional case, and depends on several parameters involved. © by Theta, 2017.
Registro:
Documento: |
Artículo
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Título: | Hypercyclic behavior of some non-convolution operators on H(CN) |
Autor: | Muro, S.; Pinasco, D.; Savransky, M. |
Filiación: | Departamento de Matemática - Pab I, Facultad De Cs. Exactas Y Naturales, Universidad de Buenos Aires, (1428), Ciudad Autónoma de Buenos Aires, Argentina Departamento de Matemáticas Y Estadística, Universidad Torcuato di Tella, Av. Figueroa Alcorta 7350, (1428), Ciudad Autónoma de Buenos Aires, Argentina
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Palabras clave: | Composition operators; Differentiation operators; Frequently hypercyclic operators; Non-convolution operators; Strongly mixing operators |
Año: | 2017
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Volumen: | 77
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Número: | 1
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Página de inicio: | 39
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Página de fin: | 59
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DOI: |
http://dx.doi.org/10.7900/jot.2015oct08.2127 |
Título revista: | Journal of Operator Theory
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Título revista abreviado: | J. Oper. Theory
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ISSN: | 03794024
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v77_n1_p39_Muro |
Referencias:
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- Bayart, F., Matheron, E., Mixing operators and small subsets of the circle (2016) J. Reine Angew. Math, 715, pp. 75-123
- Bernal-González, L., Universal entire functions for affine endomorphisms of CN (2005) J. Math. Anal. Appl, 305, pp. 690-697
- Bernal-González, L., Montes-Rodríguez, A., Universal functions for composition operators (1995) Complex Variables Theory Appl, 27, pp. 47-56
- Birkhoff, G.D., Démonstration d'un théorème élémentaire sur les fonctions entières (1929) C. R. Acad. Sci. Paris, 189, pp. 473-475
- Bonilla, A., Grosse-Erdmann, K.-G., On a theorem of Godefroy and Shapiro (2006) Integral Equations Operator Theory, 56, pp. 151-162
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- Godefroy, G., Shapiro, J.H., Operators with dense, invariant, cyclic vector manifolds (1991) J. Funct. Anal, 98, pp. 229-269
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- Murillo-Arcila, M., Peris, A., Strong mixing measures for linear operators and frequent hypercyclicity (2013) J. Math. Anal. Appl, 398, pp. 462-465
- Muro, S., Pinasco, D., Savransky, M., Strongly mixing convolution operators on Fréchet spaces of holomorphic functions (2014) Integral Equations Operator Theory, 80, pp. 453-468
- Petersson, H., Supercyclic and hypercyclic non-convolution operators (2006) J. Operator Theory, 55, pp. 135-152
Citas:
---------- APA ----------
Muro, S., Pinasco, D. & Savransky, M.
(2017)
. Hypercyclic behavior of some non-convolution operators on H(CN). Journal of Operator Theory, 77(1), 39-59.
http://dx.doi.org/10.7900/jot.2015oct08.2127---------- CHICAGO ----------
Muro, S., Pinasco, D., Savransky, M.
"Hypercyclic behavior of some non-convolution operators on H(CN)"
. Journal of Operator Theory 77, no. 1
(2017) : 39-59.
http://dx.doi.org/10.7900/jot.2015oct08.2127---------- MLA ----------
Muro, S., Pinasco, D., Savransky, M.
"Hypercyclic behavior of some non-convolution operators on H(CN)"
. Journal of Operator Theory, vol. 77, no. 1, 2017, pp. 39-59.
http://dx.doi.org/10.7900/jot.2015oct08.2127---------- VANCOUVER ----------
Muro, S., Pinasco, D., Savransky, M. Hypercyclic behavior of some non-convolution operators on H(CN). J. Oper. Theory. 2017;77(1):39-59.
http://dx.doi.org/10.7900/jot.2015oct08.2127