Previous issue ·  Next issue ·  Most recent issue in the archive · All issues in the archive   

Journal of Operator Theory

Volume 52, Issue 1, Summer 2004  pp. 185-214.

Dynamics of properties of Toeplitz operators on the upper-half plane: parabolic case

Authors:  S. Grudsky, (1) A. Karapetyants, (2) and N. Vasilevski (3)
Author institution: (1) Departamento de Matematicas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000 Mexico, D.F., Mexico
(2) Departamento de Matematicas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000 Mexico, D.F., Mexico
(3) Departamento de Matematicas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000 Mexico, D.F., Mexico


Summary:  We consider Toeplitz operators $T_a^{(\lambda)}$ acting on the weighted Bergman spaces $\Aa_\lambda^2(\Pi)$, $\lambda \in [0,\infty)$, over the upper half-plane $\Pi,$ whose symbols depend on $y=\im z$. Motivated by the Berezin quantization procedure we study the dependence of the properties of such operators on the weight $\lambda$ and, in particular, under the limit procedure $\lambda\rightarrow\infty$.

Keywords:  Weighted Bergman spaces, Toeplitz operator, boundedness, spectrum


Contents    Full-Text PDF