Details
| Original language | English |
|---|---|
| Pages (from-to) | 271-299 |
| Number of pages | 29 |
| Journal | Integral Equations and Operator Theory |
| Volume | 81 |
| Issue number | 2 |
| Publication status | Published - 11 Dec 2014 |
Abstract
We define a family of associative products (Formula Presented) on a space S∞ of real analytic functions on (Formula Presented) that are contained in the range of the heat transform for all times t > 0. Extending results in Bauer (J Funct Anal 256:3107–3142, 2009), Coburn (J Funct Anal 161:509–525, 1999; Proc Am Math Soc 129(11):3331–3338, 2007) we show that this product leads to composition formulas of in general unbounded Berezin–Toeplitz operators (Formula Presented) denotes the Segal–Bargmann space over (Formula Presented) with respect to the semi-classical parameter s > 0. In the special case of operators with polynomial symbols or for products of just two operators such formulas previously have been obtained in Bauer (J Funct Anal 256:3107–3142, 2009), Coburn (Proc Am Math Soc 129(11):3331–3338, 2007), respectively. Finally we give an example of a bounded real analytic function h on (Formula Presented) such that (Formula Presented) cannot be expressed in form of a Toeplitz operator (Formula Presented) where g fulfills a certain growth condition at infinity.
Keywords
- *-product in deformation quantization, Berezin transform, Berezin–Toeplitz quantization, composition formulas, Fock space
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 81, No. 2, 11.12.2014, p. 271-299.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Heat Flow and An Algebra of Toeplitz Operators
AU - Agbor, Dieudonne
AU - Bauer, Wolfram
N1 - Publisher Copyright: © 2014, Springer Basel. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2014/12/11
Y1 - 2014/12/11
N2 - We define a family of associative products (Formula Presented) on a space S∞ of real analytic functions on (Formula Presented) that are contained in the range of the heat transform for all times t > 0. Extending results in Bauer (J Funct Anal 256:3107–3142, 2009), Coburn (J Funct Anal 161:509–525, 1999; Proc Am Math Soc 129(11):3331–3338, 2007) we show that this product leads to composition formulas of in general unbounded Berezin–Toeplitz operators (Formula Presented) denotes the Segal–Bargmann space over (Formula Presented) with respect to the semi-classical parameter s > 0. In the special case of operators with polynomial symbols or for products of just two operators such formulas previously have been obtained in Bauer (J Funct Anal 256:3107–3142, 2009), Coburn (Proc Am Math Soc 129(11):3331–3338, 2007), respectively. Finally we give an example of a bounded real analytic function h on (Formula Presented) such that (Formula Presented) cannot be expressed in form of a Toeplitz operator (Formula Presented) where g fulfills a certain growth condition at infinity.
AB - We define a family of associative products (Formula Presented) on a space S∞ of real analytic functions on (Formula Presented) that are contained in the range of the heat transform for all times t > 0. Extending results in Bauer (J Funct Anal 256:3107–3142, 2009), Coburn (J Funct Anal 161:509–525, 1999; Proc Am Math Soc 129(11):3331–3338, 2007) we show that this product leads to composition formulas of in general unbounded Berezin–Toeplitz operators (Formula Presented) denotes the Segal–Bargmann space over (Formula Presented) with respect to the semi-classical parameter s > 0. In the special case of operators with polynomial symbols or for products of just two operators such formulas previously have been obtained in Bauer (J Funct Anal 256:3107–3142, 2009), Coburn (Proc Am Math Soc 129(11):3331–3338, 2007), respectively. Finally we give an example of a bounded real analytic function h on (Formula Presented) such that (Formula Presented) cannot be expressed in form of a Toeplitz operator (Formula Presented) where g fulfills a certain growth condition at infinity.
KW - -product in deformation quantization
KW - Berezin transform
KW - Berezin–Toeplitz quantization
KW - composition formulas
KW - Fock space
UR - http://www.scopus.com/inward/record.url?scp=84925521498&partnerID=8YFLogxK
U2 - 10.1007/s00020-014-2205-2
DO - 10.1007/s00020-014-2205-2
M3 - Article
AN - SCOPUS:84925521498
VL - 81
SP - 271
EP - 299
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 2
ER -