- -

Power bounded composition operators on spaces of analytic functions

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Power bounded composition operators on spaces of analytic functions

Mostrar el registro completo del ítem

Bonet Solves, JA.; Domanski, P. (2011). Power bounded composition operators on spaces of analytic functions. Collectanea Mathematica. 62(1):69-83. https://doi.org/10.1007/s13348-010-0005-9

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/40480

Ficheros en el ítem

Metadatos del ítem

Título: Power bounded composition operators on spaces of analytic functions
Autor: Bonet Solves, José Antonio Domanski, P.
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
We study the dynamical behaviour of composition operators defined on spaces of real analytic functions. We characterize when such operators are power bounded, i.e. when the orbits of all the elements are bounded. In this ...[+]
Palabras clave: Composition operator , Hyperbolic spaces , Hypercyclic operator , Mean ergodic operator , Orbit , Power bounded operator , Real analytic manifold , Spaces of real analytic functions
Derechos de uso: Reserva de todos los derechos
Fuente:
Collectanea Mathematica. (issn: 0010-0757 )
DOI: 10.1007/s13348-010-0005-9
Editorial:
Springer Milan
Versión del editor: http://dx.doi.org/10.1007/s13348-010-0005-9
Código del Proyecto:
info:eu-repo/grantAgreement/MEC//MTM2007-62643/ES/METODOS DE ANALISIS FUNCIONAL PARA EL ANALISIS COMPLEJO Y LAS ECUACIONES EN DERIVADAS PARCIALES/
info:eu-repo/grantAgreement/GVA//PROMETEO08%2F2008%2F101/ES/Análisis funcional, teoría de operadores y aplicaciones/
info:eu-repo/grantAgreement/MNiSW//NN201 2740 33/
Agradecimientos:
The research of Bonet was partially supported by MEC and FEDER Project MTM2007-62643 and by GV Project Prometeo/2008/101. The research of Domanski was supported in years 2007-2010 by Ministry of Science and Higher Education, ...[+]
Tipo: Artículo

References

Abate, M.: Iteration Theory of Holomorphic Maps on Taut Manifolds. Mediterranean Press, Commenda di Rende (1989)

Albanese A.A., Bonet J., Ricker W.J.: On mean ergodic operators. In: Curbera G.P.et. al., (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser Verlag, Basel (2009)

Albanese A.A., Bonet J., Ricker W.J.: Mean ergodic operators in Fréchet spaces. Anal. Acad. Sci. Fenn. Math. 34, 401–436 (2009) [+]
Abate, M.: Iteration Theory of Holomorphic Maps on Taut Manifolds. Mediterranean Press, Commenda di Rende (1989)

Albanese A.A., Bonet J., Ricker W.J.: On mean ergodic operators. In: Curbera G.P.et. al., (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser Verlag, Basel (2009)

Albanese A.A., Bonet J., Ricker W.J.: Mean ergodic operators in Fréchet spaces. Anal. Acad. Sci. Fenn. Math. 34, 401–436 (2009)

Bayart F., Matheron E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)

Bernal-González L., Montes-Rodríguez A.: Universal functions for composition operators. Complex Variables 27, 47–56 (1995)

Bernal-González L.: Universal entire functions for affine endomorphisms of $${\mathbb{C}^{\mathbb{N}}}$$ . J. Math. Anal. Appl. 305, 690–697 (2005)

Bonet J., Domański P.: Real analytic curves in Fréchet spaces and their duals. Mh. Math. 126, 13–36 (1998)

Bonet J., Domański P.: The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations. Adv. Math. 217, 561–585 (2008)

Bonet, J., Domański, P.: A note on mean ergodic composition operators on spaces of holomorphic functions. Rev. R. Acad. Cien. Ser. A Mat. RACSAM (to appear)

Cascales B., Ka̧kol J., Saxon S.A.: Metrizability vs. Fréchet-Urysohn property. Proc. Am. Math. Soc. 131, 3623–3631 (2003)

Cowen, C.C., MacCluer, B.D.: Composition operators on spaces of analytic functions. In: Studies in Advanced Mathematics. CRC Press, Boca Raton (1995)

Domański, P.: Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives. In: Ciesielski, Z., Pełczyński, A., Skrzypczak, L. (eds.) Orlicz Centenary Volume, vol. 64, pp. 51–70. Banach Center Publications, Institute of Mathematics, Warszawa (2004)

Domański P.: Real analytic parameter dependence of solutions of differential equations. Rev. Mat. Iberoamericana 26, 175–238 (2010)

Domański, P.: Notes on real analytic functions and classical operators. Lecture Notes for Winter School in Complex Analysis and Operator Theory, Valencia (preprint, 2010). http://amu.edu.pl/~domanski/valenciawinter10/Articlemode.pdf

Domański P., Langenbruch M.: Composition operators on spaces of real analytic functions. Math. Nach. 254(255), 68–86 (2003)

Domański P., Langenbruch M.: Coherent analytic sets and composition of real analytic functions. J. Reine Angew. Math. 582, 41–59 (2005)

Domański P., Langenbruch M.: Composition operators with closed image on spaces of real analytic functions. Bull. Lond. Math. Soc. 38, 636–646 (2006)

Domański P., Vogt D.: The space of real analytic functions has no basis. Stud. Math. 142, 187–200 (2000)

Domański, P., Vogt, D.: Linear topological properties of the space of real analytic functions on the real line. In: Bierstedt, K.D., Bonet, J., Maestre, M., Schmets, J., (eds.) Recent Progress in Functional Analysis, pp. 113–132. Proc. Valencia 2000, North-Holland Mathematical Studies, Amsterdam (2001)

Fonf V.P., Lin M., Wojtaszczyk P.: Ergodic characterizations of reflexivity in Banach spaces. J. Funct. Anal. 187, 146–162 (2001)

Grosse-Erdmann K.G.: Universal families and hypercyclic operators. Bull. Am. Math. Soc. 36, 345–381 (1999)

Grosse-Erdmann K.G., Mortini R.: Universal functions for composition operators with non-automorphic symbol. J. d’Analyse Math. 107, 355–376 (2009)

Grosse-Erdmann, K.G., Peris, A.: Linear Chaos. Springer, Berlin (to appear, 2010)

Guaraldo, F., Macrì, P., Tancredi, A.: Topics on Real Analytic Spaces. Vieweg, Braunschweig (1986)

Gunning R.C.: Introduction to Holomorphic Functions of Several Variables. Wadsworth & Brooks/Cole, Belmont (1990)

Hörmander L.: An Introduction to Complex Analysis in Several Variables, 3rd edn. Elsevier, North-Holland, Amsterdam (1990)

Kobayashi S.: Hyperbolic Complex Spaces. Springer, Berlin (1998)

Krantz S.: Function Theory of Several Complex Variables. Wiley, New York (1982)

Krengel U.: Ergodic Theorems. de Gruyter, Berlin (1985)

Kriegl A., Michor P.W.: The convenient setting for real analytic mappings. Acta Math. 165, 105–159 (1990)

Kriegl A., Michor P.W.: The Convenient Setting of Global Analysis. American Mathematical Society, Providence (1997)

Langenbruch M.: Analytic extension of smooth functions. Results Math. 36, 281–296 (1999)

Langenbruch M.: Characterization of surjective partial differential operators on spaces of real analytic functions. Stud. Math. 162, 53–96 (2004)

Lee J.M.: Introduction to Smooth Manifolds. Springer, New York (2003)

Meise R., Vogt D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)

Milnor J.: Dynamics in One Complex Variable. Vieweg, Braunschweig (2006)

Shapiro J.H.: Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics. Springer, New York (1993)

Shapiro, J.H.: Notes on the dynamics of linear operators. Lecture notes. http://www.mth.msu.edu/~shapiro/Pubvit/Downloads/LinDynamics/LynDynamics.html

Vogt D.: Extension operators for real analytic functions on compact subvarieties of $${\mathbb{R}\sp d}$$ . J. Reine Angew. Math. 606, 217–233 (2007)

Vogt D.: Section spaces of real analytic vector bundles and a theorem of Grothendieck and Poly. In: Kaminski, A., Oberguggenberger, M., Pilipovic, S. (eds) Generalized Functions and its Applications, vol. 88, pp. 315–321. Banach Center Publication, Warszawa (2010)

Yosida K.: Functional Analysis. Springer, Heidelberg (1965)

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem