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Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions

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Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions

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dc.contributor.author Bonet Solves, José Antonio es_ES
dc.contributor.author Domanski, Pawel es_ES
dc.date.accessioned 2016-10-05T17:37:29Z
dc.date.available 2016-10-05T17:37:29Z
dc.date.issued 2015-04
dc.identifier.issn 0378-620X
dc.identifier.uri http://hdl.handle.net/10251/71248
dc.description.abstract We obtain full description of eigenvalues and eigenvectors of composition operators Cϕ : A (R) → A (R) for a real analytic self map ϕ : R → R as well as an isomorphic description of corresponding eigenspaces. We completely characterize those ϕ for which Abel’s equation f ◦ ϕ = f + 1 has a real analytic solution on the real line. We find cases when the operator Cϕ has roots using a constructed embedding of ϕ into the so-called real analytic iteration semigroups. es_ES
dc.description.sponsorship (1) The research of the authors was partially supported by MEC and FEDER Project MTM2010-15200 and MTM2013-43540-P and the work of Bonet also by GV Project Prometeo II/2013/013. The research of Domanski was supported by National Center of Science, Poland, Grant No. NN201 605340. (2) The authors are very indebted to K. Pawalowski (Poznan) for providing us with references [26,27,47] and also explaining some topological arguments of [10]. The authors are also thankful to M. Langenbruch (Oldenburg) for providing a copy of [29]. en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Integral Equations and Operator Theory es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Spaces of real analytic functions es_ES
dc.subject Composition operator es_ES
dc.subject Eigenvalues and eigenvectors es_ES
dc.subject Spectrum es_ES
dc.subject Abel's functional equation es_ES
dc.subject Iteration semigroup es_ES
dc.subject Iteration root es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00020-014-2175-4
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2010-15200/ES/METODOS DE ANALISIS FUNCIONAL PARA EL ANALISIS MATEMATICO/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2013-43540-P/ES/METODOS DEL ANALISIS FUNCIONAL Y TEORIA DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEOII%2F2013%2F013/ES/Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NCN//N N201 605340/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Arquitectura - Escola Tècnica Superior d'Arquitectura es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada es_ES
dc.description.bibliographicCitation Bonet Solves, JA.; Domanski, P. (2015). Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions. Integral Equations and Operator Theory. 81(4):455-482. https://doi.org/10.1007/s00020-014-2175-4 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s00020-014-2175-4 es_ES
dc.description.upvformatpinicio 455 es_ES
dc.description.upvformatpfin 482 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 81 es_ES
dc.description.issue 4 es_ES
dc.relation.senia 300624 es_ES
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.contributor.funder National Science Centre, Polonia es_ES
dc.description.references Abel, N.H.: Determination d’une function au moyen d’une equation qui ne contient qu’une seule variable. In: Oeuvres Complètes, vol. II, pp. 246-248. Christiania (1881) es_ES
dc.description.references Baker I.N.: Zusammensetzung ganzer Funktionen. Math. Z. 69, 121–163 (1958) es_ES
dc.description.references Baker I.N.: Permutable power series and regular iteration. J. Aust. Math. Soc. 2, 265–294 (1961) es_ES
dc.description.references Baker I.N.: Permutable entire functions. Math. Z. 79, 243–249 (1962) es_ES
dc.description.references Baker I.N.: Fractional iteration near a fixpoint of multiplier 1. J. Aust. Math. Soc. 4, 143–148 (1964) es_ES
dc.description.references Baker I.N.: Non-embeddable functions with a fixpoint of multiplier 1. Math. Z. 99, 337–384 (1967) es_ES
dc.description.references Baker I.N.: On a class of nonembeddable entire functions. J. Ramanujan Math. Soc. 3, 131–159 (1988) es_ES
dc.description.references Baron K., Jarczyk W.: Recent results on functional equations in a single variable, perspectives and open problems. Aequ. Math. 61, 1–48 (2001) es_ES
dc.description.references Belitskii G., Lyubich Y.: The Abel equation and total solvability of linear functional equations. Studia Math. 127, 81–97 (1998) es_ES
dc.description.references Belitskii G., Lyubich Yu.: The real analytic solutions of the Abel functional equation. Studia Math. 134, 135–141 (1999) es_ES
dc.description.references Belitskii G., Tkachenko V.: One-Dimensional Functional Equations. Springer, Basel (2003) es_ES
dc.description.references Belitskii G., Tkachenko V.: Functional equations in real analytic functions. Studia Math. 143, 153–174 (2000) es_ES
dc.description.references Bonet J., Domański P.: Power bounded composition operators on spaces of analytic functions. Collect. Math. 62, 69–83 (2011) es_ES
dc.description.references Bonet J., Domański P.: Hypercyclic composition operators on spaces of real analytic functions. Math. Proc. Camb. Philos. Soc. 153, 489–503 (2012) es_ES
dc.description.references Bracci, F., Poggi-Corradini, P.: On Valiron’s theorem. In: Proceedings of Future Trends in Geometric Function Theory. RNC Workshop Jyväskylä 2003, Rep. Univ. Jyväskylä Dept. Math. Stat., vol. 92, pp. 39–55 (2003) es_ES
dc.description.references Contreras, M.D.: Iteración de funciones analíticas en el disco unidad. Universidad de Sevilla (2009). (Preprint) es_ES
dc.description.references Contreras M.D., Díaz-Madrigal S., Pommerenke Ch.: Some remarks on the Abel equation in the unit disk. J. Lond. Math. Soc. 75(2), 623–634 (2007) es_ES
dc.description.references Cowen C.: Iteration and the solution of functional equations for functions analytic in the unit disc. Trans. Am. Math. Soc. 265, 69–95 (1981) es_ES
dc.description.references Cowen C.C., MacCluer B.D.: Composition operators on spaces of analytic functions. In: Studies in Advanced Mathematics. CRC Press, Boca Raton (1995) es_ES
dc.description.references Domański, P.: Notes on real analytic functions and classical operators. In: Topics in Complex Analysis and Operator Theory (Winter School in Complex Analysis and Operator Theory, Valencia, February 2010). Contemporary Math., vol. 561, pp. 3–47. Am. Math. Soc., Providence (2012) es_ES
dc.description.references Domański P., Goliński M., Langenbruch M.: A note on composition operators on spaces of real analytic functions. Ann. Polon. Math. 103, 209–216 (2012) es_ES
dc.description.references P. Domański M. Langenbruch 2003 Language="En"Composition operators on spaces of real analytic functions Math. Nachr. 254–255, 68–86 (2003) es_ES
dc.description.references Domański P., Langenbruch M.: Coherent analytic sets and composition of real analytic functions. J. Reine Angew. Math. 582, 41–59 (2005) es_ES
dc.description.references Domański P., Langenbruch M.: Composition operators with closed image on spaces of real analytic functions. Bull. Lond. Math. Soc. 38, 636–646 (2006) es_ES
dc.description.references Domański P., Vogt D.: The space of real analytic functions has no basis. Studia Math. 142, 187–200 (2000) es_ES
dc.description.references Fuks D.B., Rokhlin V.A.: Beginner’s Course in Topology. Springer, Berlin (1984) es_ES
dc.description.references Greenberg M.J.: Lectures on Algebraic Topology. W. A. Benjamin Inc., Reading (1967) es_ES
dc.description.references Hammond, C.: On the norm of a composition operator, PhD. dissertation, Graduate Faculty of the University of Virginia (2003). http://oak.conncoll.edu/cnham/Thesis.pdf es_ES
dc.description.references Handt T., Kneser H.: Beispiele zur Iteration analytischer Funktionen. Mitt. Naturwiss. Ver. für Neuvorpommernund Rügen, Greifswald 57, 18–25 (1930) es_ES
dc.description.references Heinrich T., Meise R.: A support theorem for quasianalytic functionals. Math. Nachr. 280(4), 364–387 (2007) es_ES
dc.description.references Karlin S., McGregor J.: Embedding iterates of analytic functions with two fixed points into continuous group. Trans.Am. Math. Soc. 132, 137–145 (1968) es_ES
dc.description.references Kneser H.: Reelle analytische Lösungen der Gleichung $${\varphi(\varphi(x))=e^x}$$ φ ( φ ( x ) ) = e x und verwandter Funktionalgleichungen. J. Reine Angew. Math. 187, 56–67 (1949) es_ES
dc.description.references Königs, G.: Recherches sur les intégrales de certaines équations fonctionnelles. Ann. Sci. Ecole Norm. Sup. (3) 1, Supplément, 3–41 (1884) es_ES
dc.description.references Kuczma M.: Functional Equations in a Single Variable. PWN-Polish Scientific Publishers, Warszawa (1968) es_ES
dc.description.references Kuczma M., Choczewski B., Ger R.: Iterative Functional Equations. Cambridge University Press, Cambridge (1990) es_ES
dc.description.references Meise R., Vogt D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997) es_ES
dc.description.references Milnor, J.: Dynamics in One Complex Variable. Vieweg, Braunschweig (2006) es_ES
dc.description.references Schröder E.: über iterierte Funktionen. Math. Ann. 3, 296–322 (1871) es_ES
dc.description.references Shapiro J.H.: Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics. Springer, New York (1993) es_ES
dc.description.references Shapiro, J.H.: Notes on the dynamics of linear operators. Lecture Notes. http://www.mth.msu.edu/~hapiro/Pubvit/Downloads/LinDynamics/LynDynamics.html es_ES
dc.description.references Shapiro, J.H.: Composition operators and Schröder functional equation. In: Studies on Composition Operators (Laramie, WY, 1996), Contemp. Math., vol. 213, pp. 213–228. Am. Math. Soc., Providence (1998) es_ES
dc.description.references Szekeres G.: Regular iteration of real and complex functions. Acta Math. 100, 203–258 (1958) es_ES
dc.description.references Szekeres G.: Fractional iteration of exponentially growing functions. J. Aust. Math. Soc. 2, 301–320 (1961) es_ES
dc.description.references Szekeres G.: Fractional iteration of entire and rational functions. J. Aust. Math. Soc. 4, 129–142 (1964) es_ES
dc.description.references Szekeres G.: Abel’s equations and regular growth: variations on a theme by Abel. Exp. Math. 7, 85–100 (1998) es_ES
dc.description.references Trappmann H., Kouznetsov D.: Uniqueness of holomorphic Abel function at a complex fixed point pair. Aequ. Math. 81, 65–76 (2011) es_ES
dc.description.references Viro, O.: 1-manifolds. Bull. Manifold Atlas. http://www.boma.mpim-bonn.mpg.de/articles/48 (a prolonged version also http://www.map.mpim-bonn.mpg.de/1-manifolds#Differential_structures ) es_ES
dc.description.references Walker P.L.: A class of functional equations which have entire solutions. Bull. Aust. Math. Soc. 39, 351–356 (1988) es_ES
dc.description.references Walker P.L.: The exponential of iteration of e x −1. Proc. Am. Math. Soc. 110, 611–620 (1990) es_ES
dc.description.references Walker P.L.: On the solution of an Abelian functional equation. J. Math. Anal. Appl. 155, 93–110 (1991) es_ES
dc.description.references Walker P.L.: Infinitely differentiable generalized logarithmic and exponential functions. Math. Comp. 57, 723–733 (1991) es_ES


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