Harmonic Analysis on Quantum Complex Hyperbolic Spaces

被引：0
|
作者：
Bershtein, Olga [1 ]
Kolisnyk, Yevgen [1 ]
机构：
[1] Inst Low Temp Phys & Engn, UA-61103 Kharkov, Ukraine
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2011年 / 7卷
关键词：
quantum groups; harmonic analysis on quantum symmetric spaces; q-difference operators; Al-Salam-Chihara polynomials; Plancherel formula; SPHERICAL-FUNCTIONS; FORMULA;
D O I：
10.3842/SIGMA.2011.078
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order q-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.
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页数：19
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