Search RiuNet
This Collection

# A Note on the Spectrum of Composition Operators on Spaces of Real Analytic Functions

Bonet Solves, JA.; Domanski, P. (2017). A Note on the Spectrum of Composition Operators on Spaces of Real Analytic Functions. Complex Analysis and Operator Theory. 11(1):161-174. https://doi.org/10.1007/s11785-016-0589-5

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/149725

## Files in this item

Title: A Note on the Spectrum of Composition Operators on Spaces of Real Analytic Functions
Author:
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
 2017-01
Abstract:
[EN] In this paper the spectrum of composition operators on the space of real analytic functions is investigated. In some cases it is completely determined while in some other cases it is only estimated.
Subjects:
Copyrigths: Reserva de todos los derechos
Source:
Complex Analysis and Operator Theory. (issn: 1661-8254 )
DOI: 10.1007/s11785-016-0589-5
Publisher:
Springer-Verlag
Publisher version: https://doi.org/10.1007/s11785-016-0589-5
Project ID:
info:eu-repo/grantAgreement/NCN//DEC-2013%2F10%2FA%2FST1%2F00091/
info:eu-repo/grantAgreement/GVA//PROMETEOII%2F2013%2F013/ES/Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)/
info:eu-repo/grantAgreement/MINECO//MTM2013-43540-P/ES/METODOS DEL ANALISIS FUNCIONAL Y TEORIA DE OPERADORES/
Thanks:
The research of the authors was partially supported by MEC and FEDER Project MTM2013-43540-P and the work of of Bonet by the Grant GV Project Prometeo II/2013/013. The research of Domanski was supported by National Center ...[+]
Type: Artículo

## References

Belitskii, G., Lyubich, Y.: The Abel equation and total solvability of linear functional equations. Studia Math. 127, 81–97 (1998)

Belitskii, G., Lyubich, Y.: The real analytic solutions of the Abel functional equation. Studia Math. 134, 135–141 (1999)

Belitskii, G., Tkachenko, V.: One-Dimensional Functional Equations. Springer, Basel (2003) [+]
Belitskii, G., Lyubich, Y.: The Abel equation and total solvability of linear functional equations. Studia Math. 127, 81–97 (1998)

Belitskii, G., Lyubich, Y.: The real analytic solutions of the Abel functional equation. Studia Math. 134, 135–141 (1999)

Belitskii, G., Tkachenko, V.: One-Dimensional Functional Equations. Springer, Basel (2003)

Belitskii, G., Tkachenko, V.: Functional equations in real analytic functions. Studia Math. 143, 153–174 (2000)

Bonet, J., Domański, P.: Power bounded composition operators on spaces of analytic functions. Collect. Math. 62, 69–83 (2011)

Bonet, J., Domański, P.: Hypercyclic composition operators on spaces of real analytic fucntions. Math. Proc. Cambridge Phil. Soc. 153, 489–503 (2012)

Bonet, J., Domański, P.: Abel’s functional equation and eigenvalues of composition operators on spaces of real analytic functions. Integr. Equ. Oper. Theor. 81, 455–482 (2015). doi: 10.1007/s00020-014-2175-4

Cartan, H.: Variétés analytiques réelles et variétés analytiques complexes. Bull. Soc. Math. France 85, 77–99 (1957)

Domański, P.: Notes on real analytic functions and classical operators, Topics in Complex Analysis and Operator Theory (Winter School in Complex Analysis and Operator Theory, Valencia, February 2010), Contemporary Math. 561 (2012) 3–47. Amer. Math. Soc, Providence (2012)

Domański, P., Goliński, M., Langenbruch, M.: A note on composition operators on spaces of real analytic functions. Ann. Polon. Mat. 103, 209–216 (2012)

Domański, P., Langenbruch, M.: Composition operators on spaces of real analytic functions. Math. Nachr. 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. Studia Math. 142, 187–200 (2000)

Hörmander, L.: An Introduction to Complex Analysis in Several Variables. North Holland, Amsterdam (1986)

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

Smajdor, W.: On the existence and uniqueness of analytic solutions of the functional equation $$\varphi (z)=h(z,\varphi [f(z)])$$ φ ( z ) = h ( z , φ [ f ( z ) ] ) . Ann. Polon. Math. 19, 37–45 (1967)

[-]