Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Composition operators on spaces of entire functions


Authors: Gerardo A. Chacón, Gerardo R. Chacón and José Giménez
Journal: Proc. Amer. Math. Soc. 135 (2007), 2205-2218
MSC (2000): Primary 47B33; Secondary 47B38, 47A16, 32A15
DOI: https://doi.org/10.1090/S0002-9939-07-08764-3
Published electronically: March 2, 2007
MathSciNet review: 2299498
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study composition operators on spaces of entire functions. We determine which entire functions induce bounded composition operators on the Paley-Wiener space, $ L_\pi^2$, and on the $ E^2(\gamma)$ spaces. In addition, we characterize compact composition operators on these spaces. We also study the cyclic properties of composition operators acting on $ L_\pi^2$.


References [Enhancements On Off] (What's this?)

  • 1. S. Azizi, D. Cochran, J. Clark, and J. McDonald: On the Preservation of Band limitedness under Non-affine Time Warping. Unpublished notes.
  • 2. S. Azizi, D. Cochran, and J.N. McDonald: On the preservation of bandlimitedness under non-affine time warping. Proceedings of the 1999 International Workshop on Sampling Theory and Applications, Loen Norway, August 1999.
  • 3. R. Boas: Entire functions. Academic Press Inc., Pub., 1954. MR 0068627 (16:914f)
  • 4. H. Bohr: Über einen satz von Edmund Landau. Scripta Univ. Hierosolymitanarum 1, (1923).
  • 5. P. Bourdon, and J. Shapiro: Cyclic phenomena for composition operators. Mem. Amer. Math. Soc. 596 (1997). MR 1396955 (97h:47023)
  • 6. B. Carswell, B. MacCluer, and A. Schuster: Composition Operators on the Fock Space. Acta Sci. Math. (Szeged) 69 (2003), no. 3-4, 871-887. MR 2034214 (2004k:47048)
  • 7. K. Chan, and J. Shapiro: The cyclic behavior of translation operators on Hilbert spaces of entire functions. Ind. Univ. Math. J. 40 (1991) 1421-1449 MR 1142722 (92m:47060)
  • 8. J. Conway: A Course in Operator Theory. Graduate Studies in Math. Vol. 21 Amer. Math. Soc. (2000) MR 1721402 (2001d:47001)
  • 9. C. Cowen, and B. MacCluer: Composition Operators on Spaces of Analytic Functions. CRC Press, 1995. MR 1397026 (97i:47056)
  • 10. E. Gallardo-Gutiérrez, and A. Montes-Rodríguez: The role of the spectrum of the cyclic behavior of the composition operators. Memoirs of the A.M.S. 791 (2004) MR 2023381 (2004k:47050)
  • 11. A. Holland: Introduction to the theory of the entire functions. Academic Press Inc., Pub., 1973. MR 0447572 (56:5882)
  • 12. F. Jafari et al., editors: Studies on Composition Operators. Comtemp. Math. Vol. 213 American Math. Soc., 1998. MR 1601044 (98h:47005)
  • 13. B. Levin: Lectures on Entire Functions: Translations of Mathematical Monographs. Vol. 150 American Math. Soc. (1996) MR 1400006 (97j:30001)
  • 14. J. Ortega-Cerdà: Sampling measures. Publ. Mat. 42 (1998), 559-566. MR 1676043 (2000i:46023)
  • 15. G. Pólya: On an integral function of an integral function. Journal London Math. Soc., Vol. 1 (1926), 12-15.
  • 16. W. Ross, and H. Shapiro: Generalized Analytic Continuation. University Lectures Series. Vol. 25. Amer. Math. Soc. (2002) MR 1895624 (2003h:30003)
  • 17. J. Shapiro: Composition Operators and Classical Function Theory. Springer Verlag, 1993. MR 1237406 (94k:47049)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B33, 47B38, 47A16, 32A15

Retrieve articles in all journals with MSC (2000): 47B33, 47B38, 47A16, 32A15


Additional Information

Gerardo A. Chacón
Affiliation: Núcleo Táchira, Universidad de los Andes, Merida, Venezuela
Email: gchacon@cantv.net, gchacon@ula.ve

Gerardo R. Chacón
Affiliation: Facultad de Humanidades y Educación, Universidad de los Andes, Merida, Venezuela
Email: grchacon@ula.ve

José Giménez
Affiliation: Facultad de Ciencias, Universidad de los Andes, Merida, Venezuela
Email: jgimenez@ula.ve

DOI: https://doi.org/10.1090/S0002-9939-07-08764-3
Received by editor(s): February 7, 2005
Received by editor(s) in revised form: March 28, 2006
Published electronically: March 2, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society

American Mathematical Society