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Some characterizations about Generalized Hölder-Zygmund Spaces Λ_{σ,N}^{α}(R^d) Kreit, Damien ; Nicolay, Samuel E-print/Working paper (2016) Generalized Hölder-Zygmund spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ were recently introduced and are based on a generalization of Besov spaces. Under some conditions, generalized Hölder-Zygmund and ... [more ▼] Generalized Hölder-Zygmund spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ were recently introduced and are based on a generalization of Besov spaces. Under some conditions, generalized Hölder-Zygmund and Besov spaces are equal. It has been proved that most properties of classical Hölder-Zygmund spaces are held for spaces $\Lambda^{\sigma,\alpha}(\R^{d})$, which constitute a particular case of spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ with $N_{j}=2^{j}$. The goal of the present document is to prove that most of these properties are kept for $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ spaces. [less ▲] Detailed reference viewed: 9 (1 ULg)On generalized Hölder-Zygmund spaces Kreit, Damien ; Nicolay, Samuel Poster (2013, October 29) The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis. The purpose of this ... [more ▼] The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis. The purpose of this poster is to present a generalization of such spaces as well as some recent results about their characterizations. These spaces are a particular case of a generalization of Besov Spaces who have recently been extensively studied. [less ▲] Detailed reference viewed: 42 (6 ULg)Characterizations of the elements of generalized Hölder-Zygmund spaces by means of their representation Kreit, Damien ; Nicolay, Samuel in Journal of Approximation Theory (2013), 172 We give three characterizations of the elements of generalized Hölder-Zygmund spaces. The first one, based on the Littlewood-Paley decomposition is already known, but the proof given here is much simpler ... [more ▼] We give three characterizations of the elements of generalized Hölder-Zygmund spaces. The first one, based on the Littlewood-Paley decomposition is already known, but the proof given here is much simpler. The second one, based on the wavelet decompositions generalizes a result obtained by Jaffard and Meyer. The third one uses generalized interpolation spaces. These results naturally extend the ones holding for the classical Hölder-Zygmund spaces. The manuscript has been accepted for publication in Journal of Approximation Theory. [less ▲] Detailed reference viewed: 72 (19 ULg)Some characterizations of generalized Hölder spaces Kreit, Damien ; Nicolay, Samuel in Mathematische Nachrichten (2012), 285(17-18), 2157-2172 Nous démontrons dans ce papier que les propriétés classiques des espaces de Hölder sont conservées pour les espaces de Hölder généralisés en terme de suite admissible. Nous donnons en particulier des ... [more ▼] Nous démontrons dans ce papier que les propriétés classiques des espaces de Hölder sont conservées pour les espaces de Hölder généralisés en terme de suite admissible. Nous donnons en particulier des définitions équivalentes de ces espaces ainsi que des conditions d'emboitement de tels espaces. [less ▲] Detailed reference viewed: 154 (47 ULg)Quelques caractérisations des espaces de Hölder généralisés Kreit, Damien Conference (2011, November 14) Detailed reference viewed: 26 (4 ULg)Sur les espaces de Hölder ponctuels généralisés Kreit, Damien Conference (2011, September 06) We study a generalization of the well-known pointwise Hölder spaces. This generalization is based on another generalization of the (global) Hölder spaces (that we already studied and exposed on another ... [more ▼] We study a generalization of the well-known pointwise Hölder spaces. This generalization is based on another generalization of the (global) Hölder spaces (that we already studied and exposed on another seminar). We show three main characterizations of these spaces, such as a characterization by the decay of the wavelet coefficients of their elements. [less ▲] Detailed reference viewed: 33 (11 ULg)On generalized Hölder spaces Kreit, Damien ; Nicolay, Samuel Poster (2011, June) The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis and lead to natural ... [more ▼] The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis and lead to natural definitions of the notion of fractal function; for example a function belonging to $C^\alpha$ with $\alpha\in (0,1)$ typically has a fractal graph. The purpose of this poster is to present a generalization of such spaces as well as some recent results about their characterizations. [less ▲] Detailed reference viewed: 124 (20 ULg)Sur l'équation fonctionnelle de Cauchy généralisée Kreit, Damien Conference (2011, April 13) Detailed reference viewed: 50 (12 ULg)On generalized Hölder spaces Kreit, Damien Conference (2011, January 21) Detailed reference viewed: 15 (4 ULg)Some results about prevalence and strongly monoHölder functions Kreit, Damien Poster (2010, September 13) Detailed reference viewed: 13 (6 ULg) |
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