✦ LIBER ✦
Flat wavelet bases adapted to the homogeneous Sobolev spaces
✍ Scribed by Béatrice Vedel
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 241 KB
- Volume
- 282
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
We present a construction of “flat wavelet bases” adapted to the homogeneous Sobolev spaces Ḣ^s^ (ℝ^n^ ). They solve the problem of the phenomenon of infrared divergence which appears for usual wavelet expansions in Ḣ^s^ (ℝ^n^ ): these bases remove the divergence in the case s – n /2 ∉ ℕ since they are also bases of the realization of Ḣ^s^ (ℝ^n^ ). In the critical case s – n /2 ∈ ℕ, they provide a confinement of the divergence in a “small” space. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)