Berezin-Toeplitz quantization and composition formulas |
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Authors: | Wolfram Bauer |
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Affiliation: | Ernst-Moritz-Arndt-Universität Greifswald, Institut für Mathematik und Informatik, Jahnstrasse 15a, 17487 Greifswald, Germany |
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Abstract: | Extending results in [L.A. Coburn, The measure algebra of the Heisenberg group, J. Funct. Anal. 161 (1999) 509-525; L.A. Coburn, On the Berezin-Toeplitz calculus, Proc. Amer. Math. Soc. 129 (11) (2001) 3331-3338] we derive composition formulas for Berezin-Toeplitz operators with i.g. unbounded symbols in the range of certain integral transforms. The question whether a finite product of Berezin-Toeplitz operators is an operator of this type again can be answered affirmatively in several cases, but there are also well-known counter examples. We explain some consequences of such formulas to C∗-algebras generated by Toeplitz operators. |
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Keywords: | Berezin-Toeplitz operator Heat equation Berezin transform Star product |
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