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arXiv · 2011.13037

Parseval wavelet frames on Riemannian manifold

Marcin Bownik·Karol Dziedziul·Anna Kamont
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Abstract

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.

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Marcin Bownik, Karol Dziedziul, Anna Kamont. 2020-11-25. Parseval wavelet frames on Riemannian manifold. https://arxiv.org/abs/2011.13037

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