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 -