Publications Repository - Gdańsk University of Technology

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.

Authors

• prof Marcin Bownik,
• dr hab. Karol Dziedziul link open in new tab ,
• prof. dr hab. Anna Kamont link open in new tab