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 $\lambda\rightarrow\infty$.

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