Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere

Abstract We construct a single smooth orthogonal projection with desired localization whose average under group action yields the decomposition of identity operator. For any full rank lattice $$\Gamma \subset \mathbb {R}^d$$ Γ ⊂ R d , is localized in neighborhood an arbitrary precompact fundamental domain $$\mathbb {R}^d/\Gamma $$ / . also show existence highly projection, Marcinkiewicz SO ( d ), multiple on $$L^2(\mathbb {S}^{d-1})$$ L 2 ( S - 1 ) As application we continuous Parseval frames sphere.