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

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The Balian-Low theorem and regularity of Gabor systems

Authors:	Email author" target="_blank">John?J?Benedetto Email author Wojciech?Czaja Przemystaw?Gadziński Alexander?M?Powell

Institution:	(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 $\int_{\hat {\mathbb{R}}} {\left\| {\hat g(\xi )} \right\|^2 (1 + \left\| \xi \right\|^B )/\log ^d (2 + \left\| \xi \right\|)d\xi< \infty }$ .

Keywords:	Math Subject Classifications" target="_blank">Math Subject Classifications 42C40
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