Parseval Wavelet Frames on Riemannian Manifold
Parseval Wavelet Frames on Riemannian Manifold
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DOI：
10.1007/s12220-021-00742-w
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
Marcin Bownik;K. Dziedziul;A. Kamont
中科院分区：
文献类型：
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作者：
Marcin Bownik;K. Dziedziul;A. Kamont
本文对一般的黎曼流形M构造了Parseval小波框架，并证明了在中小波无条件框架的存在性。这是由于单位算子的平滑正交投影分解，这是最近由Bownik等人证明的（Potential Anal 54：41-94，2021）。我们还展示了Triebel-Lizorkinand Besovspaces紧流形上的Parseval小波框架的系数的幅度的特征。我们通过证明Hestenes算子在流形M上的有界空间上有界几何来实现这一点.
We construct Parseval wavelet frames infor a general Riemannian manifoldMand we show the existence of wavelet unconditional frames infor. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on, which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkinand Besovspaces on compact manifolds in terms of magnitudes of coefficients of Parseval wavelet frames. We achieve this by showing that Hestenes operators are bounded onandspaces on manifoldsMwith bounded geometry.