Cyclic phenomena for composition operators on weighted Bergman spaces

Anna Gori

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 529-543
  • ISSN: 0392-4033

Abstract

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In the present paper we give a generalization to the family of Bergman Spaces with weight G , A G 2 of several results, obtained in [4] for the Hardy space H 2 , concerning the cyclic and hypercyclic behaviour of composition operators CW induced by a holomorphic self map φ of the open unit disc Δ .

How to cite

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Gori, Anna. "Cyclic phenomena for composition operators on weighted Bergman spaces." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 529-543. <http://eudml.org/doc/289606>.

@article{Gori2006,
abstract = {In the present paper we give a generalization to the family of Bergman Spaces with weight $G$, $A^2_G$ of several results, obtained in [4] for the Hardy space $H^2$, concerning the cyclic and hypercyclic behaviour of composition operators CW induced by a holomorphic self map $\varphi$ of the open unit disc $\Delta \subset \mathbb\{C\}$.},
author = {Gori, Anna},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {529-543},
publisher = {Unione Matematica Italiana},
title = {Cyclic phenomena for composition operators on weighted Bergman spaces},
url = {http://eudml.org/doc/289606},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Gori, Anna
TI - Cyclic phenomena for composition operators on weighted Bergman spaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 529
EP - 543
AB - In the present paper we give a generalization to the family of Bergman Spaces with weight $G$, $A^2_G$ of several results, obtained in [4] for the Hardy space $H^2$, concerning the cyclic and hypercyclic behaviour of composition operators CW induced by a holomorphic self map $\varphi$ of the open unit disc $\Delta \subset \mathbb{C}$.
LA - eng
UR - http://eudml.org/doc/289606
ER -

References

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  1. AKEROYD, J. - KHAVINSON, D. - SHAPIRO, H. S., Remarks concerning cyclic vectors in Hardy and Bergman Spaces, Mich. Math. J., 38 (1991), 191-205. Zbl0745.30047
  2. AKEROYD, J., Polynomials approximation in the mean with respect to harmonic measure on crescents, Mich. Math. J., 39 (1992), 35-40. Zbl0755.30033
  3. BOURDON, P., Density of the polynomials in Bergman spaces, Pacific J. Math., 130 (1987), 215-221. Zbl0602.30047
  4. BOURDON, P. - SHAPIRO, H. J., Chiclic phenomena for composition operators, Memoires of the Amer. Math. Soc., 125 (1997), 69-95. 
  5. COWEN, C., Iteration and the solution of functional equations for functions analytic in the unit disc, Trans. Amer. Math. Soc., 265 (1981), 69-95. Zbl0476.30017
  6. GALLARDO GUTIERREZ, E. A. - MONTES-RODRIGUEZ, A., The Role of the Spectrum in the Cyclic Behaviour of linear fractional Composition Operators (preprint). Zbl1054.47008
  7. KRIETE, T. L., Kernel Functions and Composition Operators in Weighted Bergman Spaces, Contemporary Amer. Math. Soc., 213 (1998). Zbl0898.47028
  8. MACCLUER, B. - KRIETE, T., Composition Operators on Weighted Bergman Spaces, Indiana Math. J., 41 (1992), 755-788. Zbl0772.30043
  9. MACCLUER, B. - SHAPIRO, H. J., Angular derivatives and compact composition operators on Hardy and Bergman spaces, Canadian J. Math., 38 (1986), 878-906. Zbl0608.30050
  10. MERGELYAN, S. N., On the completeness of systems of analytic functions, AMS Transl., 19 (1962), 109-166. Zbl0122.31601
  11. SHAPIRO, H. J., Composition Operators and Classical Function Theory, Springer-Verlag, 1993. Zbl0791.30033
  12. SHIELDS, A., Weighted Shift operators and analytic function theory, Topics in Operator Theory, Mathematical Surveys, 13Amer. Math. Soc, providence R.I (1974). 

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