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See detailTopology on new sequence spaces defined with wavelet leaders
Bastin, Françoise ULg; Esser, Céline ULg; Simons, Laurent ULg

in Journal of Mathematical Analysis and Applications (2015), 431(1), 317-341

Using wavelet leaders instead of wavelet coefficients, new sequence spaces of type Sν are defined and endowed with a natural topology. Some classical topological properties are then studied; in particular ... [more ▼]

Using wavelet leaders instead of wavelet coefficients, new sequence spaces of type Sν are defined and endowed with a natural topology. Some classical topological properties are then studied; in particular, a generic result about the asymptotic repartition of the wavelet leaders of a sequence in Lν is obtained. Eventually, comparisons and links with Oscillation spaces are also presented as well as with Sν spaces. [less ▲]

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See detailTopological properties of the sequence spaces S-nu
Aubry, Jean-Marie ULg; Bastin, Françoise ULg; Dispa, S. et al

in Journal of Mathematical Analysis and Applications (2006), 321(1), 364-387

We define sequence spaces based on the distributions of the wavelet coefficients in the spirit of [S. Jaffard, Beyond Besov spaces, part I: Distributions of wavelet coefficients, J. Fourier Anal. Appl. 10 ... [more ▼]

We define sequence spaces based on the distributions of the wavelet coefficients in the spirit of [S. Jaffard, Beyond Besov spaces, part I: Distributions of wavelet coefficients, J. Fourier Anal. Appl. 10 (2004) 221-246]. We study their topology and especially show that they can be endowed with a (unique) complete metric for which compact sets can be explicitly described and we study properties of this metric. We also give relationships with Besov spaces. (c) 2005 Elsevier Inc. All rights reserved. [less ▲]

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