Parseval wavelet frames on Riemannian manifold

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 < ∞. 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 [3]. We also show a characterization of Triebel-Lizorkin F s p,q (M ) and Besov B s p,q (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.