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Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere

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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Details

Category:
Articles
Type:
artykuły w czasopismach
Published in:
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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