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Abstract
We construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank lattice \Gamma ⊂ R^d , a smooth projection is localized in a neighborhood of an arbitrary precompact fundamental domain R^d / \Gamma. We also show the existence of a highly localized smooth orthogonal projection, whose Marcinkiewicz average under the action of S O(d), is a multiple of the identity on L^2(S^{d−1}). As an application we construct highly localized continuous Parseval frames on the sphere.
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Authors (3)
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Marcin Bownik prof
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- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s00041-022-09966-y
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
no. 28,
ISSN: 1069-5869 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Bownik M., Dziedziul K., Kamont A.: Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere// JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS -Vol. 28,iss. 5 (2022),
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s00041-022-09966-y
- Verified by:
- Gdańsk University of Technology
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