Wavelet Bases for Confinements of the Infrared Divergence期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Wavelet Bases for Confinements of the Infrared Divergence

Authors:	Béatrice Vedel

Institution:	(1) LMAM, Université de Bretagne Sud, Université Européenne de Bretagne, Centre Y. Coppens, Bat. B, 1er étage, Campus de Tohannic, BP 573, 56017 Vannes, France

Abstract:	We propose the construction of wavelet bases with pseudo-polynomials adapted to the homogeneous Sobolev spaces $\dot{H}^{s}(\mathbb{R}^{n})$ , s−n/2∈ℕ. They provide a confinement of the infrared divergence by decomposing $\dot {H}^{s}(\mathbb{R}^{n})$ as a direct sum X ⊕ Y where X is a “small” space which carries the divergence and Y can be embedded in $\mathcal{S}'(\mathbb{R}^{n})$ . In the case of $\dot{H}^{1}(\mathbb{R}^{2})$ we also construct such an orthonormal basis, which provides a confinement of the Mumford process.

Keywords:	Homogeneous Sobolev spaces Wavelet bases Infrared divergence Mumford process
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