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Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces

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Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces

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dc.contributor.author Bonet Solves, José Antonio es_ES
dc.contributor.author Mengestie, Tesfa es_ES
dc.contributor.author Worku, Mafuz es_ES
dc.date.accessioned 2021-02-02T04:32:38Z
dc.date.available 2021-02-02T04:32:38Z
dc.date.issued 2019-12 es_ES
dc.identifier.issn 1422-6383 es_ES
dc.identifier.uri http://hdl.handle.net/10251/160426
dc.description.abstract [EN] Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt's resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators. es_ES
dc.description.sponsorship J. Bonet was partially supported by the research projects MTM2016-76647-P and GV Prometeo 2017/102 (Spain). M. Worku is supported by ISP project, Addis Ababa University, Ethiopia. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Results in Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Generalized Fock spaces es_ES
dc.subject Power bounded es_ES
dc.subject Uniformly mean ergodic es_ES
dc.subject Volterra-type integral operator es_ES
dc.subject Differential operator es_ES
dc.subject Hardy operator es_ES
dc.subject Supercyclic es_ES
dc.subject Hypercyclic es_ES
dc.subject Cyclic es_ES
dc.subject Ritt's resolvent condition es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00025-019-1123-7 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-76647-P/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bonet Solves, JA.; Mengestie, T.; Worku, M. (2019). Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces. Results in Mathematics. 74(4):1-15. https://doi.org/10.1007/s00025-019-1123-7 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00025-019-1123-7 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 15 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 74 es_ES
dc.description.issue 4 es_ES
dc.relation.pasarela S\404835 es_ES
dc.contributor.funder Addis Ababa University es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.description.references Abanin, A.V., Tien, P.T.: Differentiation and integration operators on weighted Banach spaces of holomorphic functions. Math. Nachr. 290(8–9), 1144–1162 (2017) es_ES
dc.description.references Atzmon, A., Brive, B.: Surjectivity and invariant subspaces of differential operators on weighted Bergman spaces of entire functions, Bergman spaces and related topics in complex analysis, Contemp. Math., vol. 404, Amer. Math. Soc., Providence, RI, pp. 27–39 (2006) es_ES
dc.description.references Bayart, F., Matheron, E.: Dynamics of Linear Operators, Cambridge Tracts in Math, vol. 179. Cambridge Univ. Press, Cambridge (2009) es_ES
dc.description.references Bermúdez, T., Bonilla, A., Peris, A.: On hypercyclicity and supercyclicity criteria. Bull. Austral. Math. Soc. 70, 45–54 (2004) es_ES
dc.description.references Beltrán, M.J.: Dynamics of differentiation and integration operators on weighted space of entire functions. Studia Math. 221, 35–60 (2014) es_ES
dc.description.references Beltrán, M.J., Bonet, J., Fernández, C.: Classical operators on weighted Banach spaces of entire functions. Proc. Am. Math. Soc. 141, 4293–4303 (2013) es_ES
dc.description.references Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999) es_ES
dc.description.references Bonet, J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 26, 649–657 (2009) es_ES
dc.description.references Bonet, J.: The spectrum of Volterra operators on weighted Banach spaces of entire functions. Q. J. Math. 66, 799–807 (2015) es_ES
dc.description.references Bonet, J., Bonilla, A.: Chaos of the differentiation operator on weighted Banach spaces of entire functions. Complex Anal. Oper. Theory 7, 33–42 (2013) es_ES
dc.description.references Bonet, J., Taskinen, J.: A note about Volterra operators on weighted Banach spaces of entire functions. Math. Nachr. 288, 1216–1225 (2015) es_ES
dc.description.references Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. Lond. Math. Soc. 47, 958–963 (2015) es_ES
dc.description.references Constantin, O., Peláez, J.-Á.: Integral operators, embedding theorems and a Littlewood–Paley formula on weighted Fock spaces. J. Geom. Anal. 26, 1109–1154 (2016) es_ES
dc.description.references De La Rosa, M., Read, C.: A hypercyclic operator whose direct sum is not hypercyclic. J. Oper. Theory 61, 369–380 (2009) es_ES
dc.description.references Dunford, N.: Spectral theory. I. Convergence to projections. Trans. Am. Math. Soc. 54, 185–217 (1943) es_ES
dc.description.references Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear Chaos. Springer, New York (2011) es_ES
dc.description.references Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233–247 (2008) es_ES
dc.description.references Krengel, U.: Ergodic Theorems. Walter de Gruyter, Berlin (1985) es_ES
dc.description.references Lyubich, Yu.: Spectral localization, power boundedness and invariant subspaces under Ritt’s type condition. Studia Mathematica 143(2), 153–167 (1999) es_ES
dc.description.references Mengestie, T.: A note on the differential operator on generalized Fock spaces. J. Math. Anal. Appl. 458(2), 937–948 (2018) es_ES
dc.description.references Mengestie, T.: Spectral properties of Volterra-type integral operators on Fock–Sobolev spaces. J. Kor. Math. Soc. 54(6), 1801–1816 (2017) es_ES
dc.description.references Mengestie, T.: On the spectrum of volterra-type integral operators on Fock–Sobolev spaces. Complex Anal. Oper. Theory 11(6), 1451–1461 (2017) es_ES
dc.description.references Mengestie, T., Ueki, S.: Integral, differential and multiplication operators on weighted Fock spaces. Complex Anal. Oper. Theory 13, 935–95 (2019) es_ES
dc.description.references Mengestie, T., Worku, M.: Isolated and essentially isolated Volterra-type integral operators on generalized Fock spaces. Integr. Transf. Spec. Funct. 30, 41–54 (2019) es_ES
dc.description.references Nagy, B., Zemanek, J.A.: A resolvent condition implying power boundedness. Studia Math. 134, 143–151 (1999) es_ES
dc.description.references Nevanlinna, O.: Convergence of iterations for linear equations. Lecture Notes in Mathematics. ETH Zürich, Birkhäuser, Basel (1993) es_ES
dc.description.references Ritt, R.K.: A condition that $$\lim _{n\rightarrow \infty } n^{-1}T^n =0$$. Proc. Am. Math. Soc. 4, 898–899 (1953) es_ES
dc.description.references Ueki, S.: Characterization for Fock-type space via higher order derivatives and its application. Complex Anal. Oper. Theory 8, 1475–1486 (2014) es_ES
dc.description.references Yosida, K.: Functional Analysis. Springer, Berlin (1978) es_ES
dc.description.references Yosida, K., Kakutani, S.: Operator-theoretical treatment of Marko’s process and mean ergodic theorem. Ann. Math. 42(1), 188–228 (1941) es_ES


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