The Balian-Low theorem and regularity of Gabor systems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

The Balian-Low theorem and regularity of Gabor systems

Authors:	John?J.?Benedetto author-information" > author-information__contact u-icon-before" > mailto:jjb@math.umd.edu" title=" jjb@math.umd.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Wojciech?Czaja,Przemystaw?Gadziński,Alexander?M.?Powell

Affiliation:	(1) Department of Mathematics, University of Maryland, 20742 College Park, MD;(2) Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract:	For any positive real numbers A, B, and d satisfying the conditions $frac{1}{A} + frac{1}{B} = 1$ , d>2, we construct a Gabor orthonormal basis for L²(ℝ), such that the generating function g∈L²(ℝ) satisfies the condition:∫_ℝ\|g(x)\|²(1+\|x\|^A)/log^d(2+\|x\|)dx < ∞ and $int_{hat {mathbb{R}}} {left\| {hat g(xi )} right\|^2 (1 + left\| xi right\|^B )/log ^d (2 + left\| xi right\|)dxi< infty }$ .

Keywords:	KeywordHeading" >Math Subject Classifications 42C40
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