Cyclic phenomena for composition operators on weighted Bergman spaces
Bollettino dell'Unione Matematica Italiana (2006)
- Volume: 9-B, Issue: 3, page 529-543
- ISSN: 0392-4041
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topGori, 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
top- 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
- AKEROYD, J., Polynomials approximation in the mean with respect to harmonic measure on crescents, Mich. Math. J., 39 (1992), 35-40. Zbl0755.30033
- BOURDON, P., Density of the polynomials in Bergman spaces, Pacific J. Math., 130 (1987), 215-221. Zbl0602.30047
- BOURDON, P. - SHAPIRO, H. J., Chiclic phenomena for composition operators, Memoires of the Amer. Math. Soc., 125 (1997), 69-95.
- 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
- GALLARDO GUTIERREZ, E. A. - MONTES-RODRIGUEZ, A., The Role of the Spectrum in the Cyclic Behaviour of linear fractional Composition Operators (preprint). Zbl1054.47008
- KRIETE, T. L., Kernel Functions and Composition Operators in Weighted Bergman Spaces, Contemporary Amer. Math. Soc., 213 (1998). Zbl0898.47028
- MACCLUER, B. - KRIETE, T., Composition Operators on Weighted Bergman Spaces, Indiana Math. J., 41 (1992), 755-788. Zbl0772.30043
- 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
- MERGELYAN, S. N., On the completeness of systems of analytic functions, AMS Transl., 19 (1962), 109-166. Zbl0122.31601
- SHAPIRO, H. J., Composition Operators and Classical Function Theory, Springer-Verlag, 1993. Zbl0791.30033
- 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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