Parseval Wavelet Frames on Riemannian Manifold

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...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of geometric analysis 2022, Vol.32 (1), Article 4
Main Authors: Bownik, Marcin, Dziedziul, Karol, Kamont, Anna
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Frames
Geometry
Global Analysis and Analysis on Manifolds
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Operators (mathematics)
Riemann manifold
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F p , q s ( M ) and Besov 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 F p , q s ( M ) and B p , q s ( M ) spaces on manifolds M with bounded geometry.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-021-00742-w