Search results for: besov spaces

• Density smoothness estimation problem using a wavelet approach

  Publication

  • K. Dziedziul
  • B. Ćmiel

  - ESAIM-Probability and Statistics - Year 2014

  In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter ). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness...

  Full text available to download

• Parseval Wavelet Frames on Riemannian Manifold

  Publication

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

  - JOURNAL OF GEOMETRIC ANALYSIS - Year 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...

  Full text available to download

• Estimation of a smoothness parameter by spline wavelets

  Publication

  • N. Jarzębkowska
  • M. Meller

  - Applicationes Mathematicae - Year 2013

  We consider the smoothness parameter s*(f) of a function f∈L2(R) in terms of Besov spaces. The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0

  Full text to download in external service

• Harmonic Analysis

  Open Research Data

  open access

  • K. Dziedziul

  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, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser...