论文标题
Riemannian歧管上的Parseval小波框架
Parseval wavelet frames on Riemannian manifold
论文作者
论文摘要
我们为一般的Riemannian歧管$ M $构建parseval小波框架，以$ l^p（m）$ $ 1 <p <\ p <\ iftty $中的$ l^2（m）$。由于$ l^2（m）$对身份操作员的平滑正交投影分解，这是可能的，这是由Arxiv的作者最近证明的：1803.03634。我们还展示了Triebel-lizorkin $ \ Mathbf f_ {p，q}^s（m）$和BESOV $ \ MATHBF B_ {我们通过表明Hestenes运营商在具有界面几何形状的歧管$ M $上实现这一目标。
We construct Parseval wavelet frames in $L^2(M)$ for a general Riemannian manifold $M$ and we show the existence of wavelet unconditional frames in $L^p(M)$ for $1 < p <\infty$. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on $L^2(M)$, which was recently proven by the authors in arXiv:1803.03634. We also show a characterization of Triebel-Lizorkin $\mathbf F_{p,q}^s(M)$ and Besov $\mathbf B_{p,q}^s(M)$ spaces on compact manifolds in terms of magnitudes of coefficients of Parseval wavelet frames. We achieve this by showing that Hestenes operators are bounded on manifolds $M$ with bounded geometry.
