整数尺度Bessel函数的多分辨小波分析
Multiresolution wavelet analysis of integer scale Bessel functions
摘要：
我们确定多分辨率子空间产生通过汉克尔变换贝塞尔函数。它们作为从几何希尔伯特空间考虑导出的正交系出现，同样的方式，来自多分辨率尺度小波构造的小波函数来自希尔伯特空间的尺度。我们研究的理论表示的$C^{\ast}$ -代数$% O_{ν+1}$所产生的多分辨率分析。发现了与马尔可夫链和$O_{ν+1}$表示的联系.由多分辨分析产生的投影值测度给出了量子群$SO_q$的马尔可夫迹.
英文摘要：
We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution scaling wavelet construction arise from a scale of Hilbert spaces. We study the theory of representations of the $C^{\ast}$-algebra $% O_{ν+1}$ arising from this multiresolution analysis. A connection with Markov chains and representations of $O_{ν+1}$ is found. Projection valued measures arising from the multiresolution analysis give rise to a Markov trace for quantum groups $SO_q$.
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