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Description
We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const. Approx., 41, 23–48 2015).
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 and Besov 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.
Dataset file
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.Example script for calculation:
https://github.com/antespi/s3md5
File details
- License:
-
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CC BYAttribution
Details
- Year of publication:
- 2021
- Verification date:
- 2021-04-26
- Dataset language:
- English
- Fields of science:
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- mathematics (Natural sciences)
- DOI:
- DOI ID 10.34808/b84g-e471 open in new tab
- Verified by:
- Gdańsk University of Technology
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