量子SU（2）群的谱分析和Haar泛函
Spectral analysis and the Haar functional on the quantum SU(2) group
摘要：
量子$SU(2)$群上的Haar泛函是群$SU(2)$上不变积分的类似物。如果限制在一个由自伴元生成的子代数上，哈尔泛函可以表示为一个具有连续测度或离散测度的积分，或者是两者的组合。利用量子$SU(2)$群的余表示理论和不可约酉余表示矩阵元的Schur正交关系，证明了Woronowicz和Koornwinder的这些结果.本文利用子代数生成元的谱分析证明了这些结果。利用Jacobi矩阵理论，谱测度可以用正交多项式的正交性测度来描述。
英文摘要：
The Haar functional on the quantum $SU(2)$ group is the analogue of invariant integration on the group $SU(2)$. If restricted to a subalgebra generated by a self-adjoint element the Haar functional can be expressed as an integral with a continuous measure or with a discrete measure or by a combination of both. These results by Woronowicz and Koornwinder have been proved by using the corepresentation theory of the quantum $SU(2)$ group and Schur's orthogonality relations for matrix elements of irreducible unitary corepresentations. These results are proved here by using a spectral analysis of the generator of the subalgebra. The spectral measures can be described in terms of the orthogonality measures of orthogonal polynomials by using the theory of Jacobi matrices.
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