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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(λ)a acting on the weighted Bergman spaces \Aa2λ(Π), λ[0,), over the upper half-plane Π, whose symbols depend on y=\imz. Motivated by the Berezin quantization procedure we study the dependence of the properties of such operators on the weight λ and, in particular, under the limit procedure λ.


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