Rok 2022

• Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere

  Publikacja

  • M. Bownik
  • K. Dziedziul
  • A. Kamont

  - JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS - Rok 2022

  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...

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Rok 2021

• Parseval Wavelet Frames on Riemannian Manifold

  Publikacja

  • M. Bownik
  • K. Dziedziul
  • A. Kamont

  - JOURNAL OF GEOMETRIC ANALYSIS - Rok 2021

  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...

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• Smooth Orthogonal Projections on Riemannian Manifold

  Publikacja

  • M. Bownik
  • K. Dziedziul
  • A. Kamont

  - POTENTIAL ANALYSIS - Rok 2021

  We construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, S´er. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser (1992), and a similar decomposition when M is the sphere by Bownik and Dziedziul (Const....

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