Berezin and Berezin-Toeplitz quantizations for general function spaces

• Autores: Miroslav Englis
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 19, Nº 2, 2006, págs. 385-430
• Idioma: inglés
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• Resumen

  • The standard Berezin and Berezin-Toeplitz quantizations on a K¿ahler 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.