Berezin and Berezin-Toeplitz quantizations for general function spaces.

Englis, Miroslav. "Berezin and Berezin-Toeplitz quantizations for general function spaces.." Revista Matemática Complutense 19.2 (2006): 385-430. <http://eudml.org/doc/41908>.

@article{Englis2006,
abstract = {The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic functions, and so on. Both positive and negative results are obtained.},
author = {Englis, Miroslav},
journal = {Revista Matemática Complutense},
keywords = {Geometría simpléctica; Espacios de Hilbert; Espacios de Sobolev; Espacios de Bergman; Operadores de Toeplitz; Berezin quantization; Berezin-Toeplitz quantization; star product; harmonic Bergman space; Sobolev-Bergman space; reproducing kernel},
language = {eng},
number = {2},
pages = {385-430},
title = {Berezin and Berezin-Toeplitz quantizations for general function spaces.},
url = {http://eudml.org/doc/41908},
volume = {19},
year = {2006},
}

TY - JOUR
AU - Englis, Miroslav
TI - Berezin and Berezin-Toeplitz quantizations for general function spaces.
JO - Revista Matemática Complutense
PY - 2006
VL - 19
IS - 2
SP - 385
EP - 430
AB - The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic functions, and so on. Both positive and negative results are obtained.
LA - eng
KW - Geometría simpléctica; Espacios de Hilbert; Espacios de Sobolev; Espacios de Bergman; Operadores de Toeplitz; Berezin quantization; Berezin-Toeplitz quantization; star product; harmonic Bergman space; Sobolev-Bergman space; reproducing kernel
UR - http://eudml.org/doc/41908
ER -