Abstract
We consider Toeplitz operators T (‚) a acting on the weighted Bergman spaces A 2(ƒ), ‚ 2 (0,1), over the upper half-plane ƒ, whose sym- bols depend on y = Imz. Motivated by the Berezin quantization procedure we study the dependence of the properties of such operators on the weight ‚ and, in particular, under the limit procedure ‚ ! 1.
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