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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Covariant derivatives of the Berezin transform


Authors: Miroslav Engliš and Renata Otáhalová
Journal: Trans. Amer. Math. Soc. 363 (2011), 5111-5129
MSC (2000): Primary 47B32; Secondary 32A36, 53B35, 32Q15
Published electronically: May 4, 2011
MathSciNet review: 2813410
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Abstract: Improving upon recent results of Coburn, Xia, Li, Engliš and Zhang, Bommier-Hato, and others, we give estimates for higher-order covariant derivatives of the Berezin transform of bounded linear operators on a reproducing kernel Hilbert space of holomorphic functions. The answer turns out to involve the curvature of the Bergman-type metric associated to the reproducing kernel.


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Additional Information

Miroslav Engliš
Affiliation: Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic – and – Mathematics Institute, Academy of Sciences, Žitná 25, 11567 Prague 1, Czech Republic
Email: englis{@}math.cas.cz

Renata Otáhalová
Affiliation: Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic
Email: Renata.Otahalova@math.slu.cz

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05111-1
PII: S 0002-9947(2011)05111-1
Keywords: Berezin transform, Berezin symbol, covariant derivative, curvature, reproducing kernel
Received by editor(s): May 16, 2008
Received by editor(s) in revised form: May 17, 2009
Published electronically: May 4, 2011
Additional Notes: This research was supported by GA AV ČR grant no. IAA100190802 and Ministry of Education research plan no. MSM4781305904
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.