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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 < ∞. 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 sp,q (M) and Besov B sp,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 F sp,q (M) and B sp,q (M) spaces on manifolds M with bounded geometry.
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Authors (3)
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Marcin Bownik prof
- University of Oregon, Eugene
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s12220-021-00742-w
- License
- Copyright (2021 Mathematica Josephina, Inc.)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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JOURNAL OF GEOMETRIC ANALYSIS
no. 32,
pages 1 - 43,
ISSN: 1050-6926 - Language:
- English
- Publication year:
- 2021
- Bibliographic description:
- Bownik M., Dziedziul K., Kamont A.: Parseval Wavelet Frames on Riemannian Manifold// JOURNAL OF GEOMETRIC ANALYSIS -Vol. 32, (2021), s.1-43
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s12220-021-00742-w
- Verified by:
- Gdańsk University of Technology
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