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See detailSpaces Snu, diametral dimension and property Omega bar
Demeulenaere, Loïc ULiege

in Journal of Mathematical Analysis and Applications (2017), 449(2), 1340-1350

This paper investigates two topological invariants in the context of the sequence spaces Snu, which are metric topological vector spaces defined in order to study the regularity of signals. First, it ... [more ▼]

This paper investigates two topological invariants in the context of the sequence spaces Snu, which are metric topological vector spaces defined in order to study the regularity of signals. First, it extends the formula already known of the diametral dimension of spaces Snu to some non-locally pseudoconvex ones. Second, it proves that locally p-convex spaces Snu verifies the property "Omega id", which is equivalent to Omega bar for Fréchet spaces. [less ▲]

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

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 ULiege; Bastin, Françoise ULiege; 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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