Details
| Original language | English |
|---|---|
| Pages (from-to) | 3107-3142 |
| Number of pages | 36 |
| Journal | Journal of functional analysis |
| Volume | 256 |
| Issue number | 10 |
| Publication status | Published - 18 Mar 2009 |
| Externally published | Yes |
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.
Keywords
- Berezin transform, Berezin-Toeplitz operator, Heat equation, Star product
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of functional analysis, Vol. 256, No. 10, 18.03.2009, p. 3107-3142.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Berezin-Toeplitz quantization and composition formulas
AU - Bauer, Wolfram
N1 - Funding Information: E-mail address: bauerwolfram@web.de. 1 Partially supported by the Grant-in-aid Scientific Research (C) No. 17540202, Japan Society for the Promotion of Science and by an Emmy-Noether grant of Deutsche Forschungsgemeinschaft. Copyright: Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009/3/18
Y1 - 2009/3/18
N2 - 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.
AB - 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.
KW - Berezin transform
KW - Berezin-Toeplitz operator
KW - Heat equation
KW - Star product
UR - http://www.scopus.com/inward/record.url?scp=62549164342&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2008.10.002
DO - 10.1016/j.jfa.2008.10.002
M3 - Article
AN - SCOPUS:62549164342
VL - 256
SP - 3107
EP - 3142
JO - Journal of functional analysis
JF - Journal of functional analysis
SN - 0022-1236
IS - 10
ER -