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Powers of hypercyclic functions for some classical hypercyclic operators

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dc.contributor.authorAron, Richard M.
dc.contributor.authorConejero, Jose A.
dc.contributor.authorSeoane-Sepúlveda, Juan B.
dc.date.accessioned2023-06-20T10:33:08Z
dc.date.available2023-06-20T10:33:08Z
dc.date.issued2007
dc.description.abstractWe show that no power of any entire function is hypercyclic for Birkhoff's translation operator on H(C). On the other hand, we see that the set of functions whose powers are all hypercyclic for MacLane's differentiation operator is a G(delta)-dense subset of H(C).
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipGVA
dc.description.sponsorshipMEC and FEDER
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/20076
dc.identifier.doi10.1007/s00020-007-1490-4
dc.identifier.issn0378-620X
dc.identifier.officialurlhttp://link.springer.com/content/pdf/10.1007%2Fs00020-007-1490-4
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50463
dc.issue.number4
dc.journal.titleIntegral Equations and Operator Theory
dc.language.isoeng
dc.page.final596
dc.page.initial591
dc.publisherBirkhauser Verlag
dc.relation.projectIDCTESPP/2005.
dc.relation.projectIDMTM2004-02262
dc.relation.projectIDMTM2006-26627-E.
dc.rights.accessRightsrestricted access
dc.subject.cdu517.98
dc.subject.keywordHypercyclic vectors
dc.subject.keywordUniversal functions.
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titlePowers of hypercyclic functions for some classical hypercyclic operators
dc.typejournal article
dc.volume.number58
dcterms.referencesR. Aron and D. Markose, On universal functions. J. Korean Math. Soc. 41 (2004),65–76. L. Bernal-Gonz´alez and A. Bonilla, Exponential type of hypercyclic entire functions. Archiv Math. 78 (2002), 283–290. G.D. Birkhoff, Demonstration d’un theoreme elementaire sur les fonctions entieres.C. R. Acad. Sci. Paris 189 (1929),473–475. C. Blair and L.A. Rubel, A universal entire function. Amer.Math. Monthly 90 (1983), 331–332. C. Blair and L.A. Rubel, A triply universal entire function. Enseign. Math. 30 (1984),269–274. A. Bonilla and K.G. Grosse-Erdmann, On a theorem of Godefroy and Shapiro. Int.Equat. Oper. Theory 56 (2006), 151-162. K.C. Chan and J.H. Shapiro, The cyclic behavior of translation operators on Hilbert spaces of entire functions. Indiana Univ. Math. J. 40 (1991), 1421–1449. J.B. Conway, Functions of One Complex Variable. Springer-Verlag, Berlin/New York, 1978. S.M. Duyos Ruiz, Universal functions and the structure of the space of entire functions.Dokl. Akad. Nauk. SSSR 279 (1984), 792–795. G. Fernandez and A.A. Hallack, Remarks on a result about hypercyclic nonconvolution operators. J. Math. Anal. Appl. 309 (2005), 52–55. G. Godefroy and J.H. Shapiro, Operators with dense,invariant, cyclic vector manifolds.J. Funct. Anal. 98 (1991), 229–269. K.G. Grosse-Erdmann, On the universal functions of G.R. MacLane. Complex Variables Theory Appl. 15 (1990), 193–196. K.G. Grosse-Erdmann, Universal families and hypercyclic operators. Bull. Amer.Math. Soc. 36 (1999), 345–381. K.G. Grosse-Erdmann, Recent developments in hypercyclicity. Rev. R. Acad. Cien.Serie A Mat. 97 (2003), 273–286. W. Luh, V.A. Martirosian, and J Muller, Universal entire functions with gap power series. Indag. Math. (N.S.) 9 (1998), 529–536. G.R. MacLane, Sequences of derivatives and normal families. J. Analyse Math.(1952), 72–87. W. Seidel and J.L. Walsh, On approximation by euclidean and non-euclidean translations of an analytic function. Bull. Amer. Math. Soc. 47 (1941), 916–920.
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