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...

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• 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...

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• 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

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