Abstract
We present an introduction to the Berezin and Berezin–Toeplitz quantizations, starting from their historical origins and relationships with other quantization methods, discussing various instructive examples like the Segal–Bargmann–Fock space, and culminating by highlights of proofs of the existence of these quantizations using both the Boutet de Monvel theory and the approach via Fefferman’s expansion and Forelli–Rudin construction. The exposition strives to be reasonably self-contained and accessible to nonexperts.
Mathematics Subject Classification (2010). Primary 53D55; Secondary 46E22, 47B35, 32A36.
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© 2016 Springer International Publishing Switzerland
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Engliš, M. (2016). An Excursion into Berezin–Toeplitz Quantization and Related Topics. In: Bahns, D., Bauer, W., Witt, I. (eds) Quantization, PDEs, and Geometry. Operator Theory: Advances and Applications(), vol 251. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22407-7_2
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DOI: https://doi.org/10.1007/978-3-319-22407-7_2
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-22406-0
Online ISBN: 978-3-319-22407-7
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