量子双曲空间上的非对易调和分析。拉普拉斯-贝尔特拉米算子
Noncommutative Harmonic Analysis on Quantum Hyperbolic Spaces. The Laplace-Beltrami Operator
摘要：
本文研究量子复双曲空间上的Laplace-Beltrami算子。我们描述了它的行动在某些$q$ -差分算子的二阶和证明谱定理这些运营商。相应的本征函数与Al-Salam-Chihara多项式有关。所得到的Plancherel测度与Harish-Chandra c函数的量子模拟有关。
英文摘要：
In this paper we study the Laplace-Beltrami operator on quantum complex hyperbolic spaces. We describe its action in terms of certain $q$-difference operators of second order and prove spectral theorems for these operators. The corresponding eigenfunctions are related to Al-Salam-Chihara polynomials. The obtained Plancherel measure is related to a quantum analog for the Harish-Chandra c-function.
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