Quantization of bounded domains |
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| Institution: | 1. Department of Mathematics and Statistics, Saint Louis University, St. Louis, MO 63103, USA;2. Lehrstuhl A für Mathematik, RWTH Aachen University, D-52056 Aachen, Germany;3. Department of Mathematics, Bridgewater State University, Bridgewater, MA 02324, USA;1. Department of Mathematics, Shantou University, Shantou, Guangdong 515063, People''s Republic of China;2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, People''s Republic of China;1. Universidade Federal do Espírito Santo, Vitória, 29075-910, ES, Brazil;2. ISMO, UMR 8214 CNRS, Univ Paris-Sud, 91405 Orsay, France;3. Laboratoire APC, UMR 7164, Univ Paris Diderot, Sorbonne Paris-Cité 75205 Paris, France;4. Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 - Rio de Janeiro, RJ, Brazil |
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| Abstract: | 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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