Berezin transform on the harmonic Fock space

被引：19

作者：

Englis, Miroslav ^{[1
,2
]}

机构：

[1] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic

[2] Silesian Univ, Math Inst, Opava 74601, Czech Republic

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 367卷 / 01期

关键词：

Berezin transform; Harmonic Fock space; Harmonic Bergman kernel; Asymptotic expansion; Horn hypergeometric functions; BERGMAN SPACES; TOEPLITZ QUANTIZATION; OPERATORS; KERNELS; UNIT;

D O I：

10.1016/j.jmaa.2009.12.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the Berezin transform associated to the harmonic Fock (Segal-Bargmann) space on C(n) has an asymptotic expansion analogously as in the holomorphic case. The proof involves a computation of the reproducing kernel, which turns out to be given by one of Horn's hypergeometric functions of two variables, and an ad hoc determination of the asymptotic behaviour of the resulting integrals, to which the ordinary stationary phase method is not directly applicable. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：75 / 97

页数：23

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[2]

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[3]

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[4]

Berezin F. A., 1974, USSR IZV, V8, P1109, DOI [10.1070/IM1974v008n05ABEH002140, DOI 10.1070/IM1974V008N05ABEH002140]