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Quantization of bounded domains

✍ Scribed by Andrea Loi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
227 KB
Volume
29
Category
Article
ISSN
0393-0440

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✦ Synopsis

We consider the quantization of a complex manifold endowed with the Bergman form following the ideas of Cahen, Gutt and Rawnsley. In particular we give a geometric interpretation for the quantization to be regular in terms of the Hilbert space of square integrable holomorphic n-forms on M and the Hilbert space of holomorphic n-forms on M bounded with respect to the Liouville element.

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We construct families of non-commuting \(\mathbb{C}^{*}\)-algebras of "quantized functions" for bounded irreducible Hermitian symmetric spaces. For this procedure, we use algebras of Toeplitz operators defined with respect to a perturbation of the ordinary Bergman metric. We prove the deformation qu