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The Berezin transform and Ha-plitz operators. (English) Zbl 0793.47026
The technique of “quantization” typically involves assigning to functions on a suitable manifold linear operators on a suitable Hilbert space. In this paper, the author provides an exposition of this technique as developed in the work of Berezin, especially as it relates to Hankel and Toeplitz operators on pseudoconvex domains in $$\mathbb{C}^ n$$. In particular, the author considers the Berezin transform in the context of Hermitian line bundles and their associated Hilbert spaces of holomorphic sections, and he discusses the principle examples and applications thereof.
The paper is written in a subjective, but refreshing, authorial voice.

##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 81S99 General quantum mechanics and problems of quantization