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Zakład Analizy Nieliniowej

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Katalog Publikacji

Rok 2023
Rok 2022
Rok 2021
  • Parseval Wavelet Frames on Riemannian Manifold
    Publikacja

    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

    - 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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Rok 2019
Rok 2015
Rok 2014
  • Density smoothness estimation problem using a wavelet approach
    Publikacja

    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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  • The smoothness test for a density function

    The problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...

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Rok 2013
Rok 2011
Rok 2010
Rok 2007
Rok 2006
Rok 2005
Rok 2004
Rok 2003
Rok 2002