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.
@article{urn:eudml:doc:41908,
title = {Berezin and Berezin-Toeplitz quantizations for general function spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {385-430},
zbl = {1122.53053},
mrnumber = {MR2241437},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41908}
}
Englis, Miroslav. Berezin and Berezin-Toeplitz quantizations for general function spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 385-430. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41908/