Reproducing Spaces and LocalizationOperators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

Reproducing Spaces and LocalizationOperators

Authors:	Shu?Jun?Dang author-information" > author-information__contact u-icon-before" > mailto:dsjun@huawei.com" title=" dsjun@huawei.com" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Li?Zhong?Peng

Affiliation:	(1) School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

Abstract:	Abstract This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators $T_{n} :L^{2} {left( R right)} to L^{2} {left( {C,e^{{ - frac{{{left\| z right\|}^{2} }} {2}}} frac{{dzdoverline{z} }} {{4pi i}}} right)}$ , s.t. $T_{n} L^{2} {left( R right)} subseteq L^{2} {left( {C,e^{{ - frac{{{left\| z right\|}^{2} }} {2}}} frac{{dzdoverline{z} }} {{4pi i}}} right)}$ are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of T _n L ²(R). Furthermore, it shows the orthogonal spaces decomposition of $L^{2} {left( {C,e^{{ - frac{{{left\| z right\|}^{2} }} {2}}} frac{{dzdoverline{z} }} {{4pi i}}} right)}$ . Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6]. Research supported by 973 Project G1999075105 and NNFS of China, Nos. 90104004 and 69735020

Keywords:	Reproducing space Localization operator Bargmann space Windowed Fourier transform
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