非均勻Gabor框架的穩(wěn)定性

唐青松,張祥德,陸小軍,朱和貴

(東北大學(xué)數(shù)學(xué)系,遼寧沈陽 110004)

非均勻Gabor框架的穩(wěn)定性

唐青松,張祥德,陸小軍,朱和貴

(東北大學(xué)數(shù)學(xué)系,遼寧沈陽 110004)

研究了當(dāng)窗函數(shù)變化時非均勻Gabor框架的穩(wěn)定性.對緊支撐Gabor框架,將均勻情況下關(guān)于穩(wěn)定性的結(jié)論推廣到了非均勻的情況;對一般的Gabor框架,利用W(L∞,‘1)范數(shù)給出了其穩(wěn)定的一個充分條件.

Gabor框架;穩(wěn)定性;Wiener混合模空間

1 引言

框架因為可為信號提供穩(wěn)定、冗余的表示而被廣泛的應(yīng)用于算子理論、非線性逼近、采樣理論、時頻分析等數(shù)學(xué)和信息科學(xué)領(lǐng)域中.Gabor框架是其中較常用的一種,它是由一個窗函數(shù)通過時頻平移產(chǎn)生的,這種特殊結(jié)構(gòu)使其十分適合于時頻分析.Gabor框架的穩(wěn)定性是指當(dāng)窗函數(shù),時移或頻移參數(shù)發(fā)生小的擾動時仍然構(gòu)成Gabor框架.Gabor框架的穩(wěn)定性在實際應(yīng)用中有重要的意義,文[1-7]對Gabor框架的穩(wěn)定性及相關(guān)問題進(jìn)行了研究,但大多是針對均勻Gabor框架的情況.隨著信息技術(shù)的發(fā)展,非均勻采樣理論引起了廣泛的關(guān)注.因此,有必要進(jìn)一步分析非均勻Gabor框架的性質(zhì).本文研究當(dāng)窗函數(shù)變化時非均勻Gabor框架的穩(wěn)定性.

首先引入一些必要的定義和引理.

2 主要結(jié)果和證明

由引理2知,{eibmxh(x?an)}也是L2(R)的一個Gabor框架.

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On the stability of irregular Gabor frames

TANG Qing-song,ZHANG Xiang-de,LU Xiao-jun,ZHU He-gui

(School of Science,Northeastern University,Shenyang110004,China)

When the window functions are changed,the stability of irregular Gabor frames are studied in this paper.The results of the stability regular Gabor frames are extended into the stability regular Gabor frames, and a sufficient conditions on the stability of irregular Gabor frames is given by W(L∞,e1).

Gabor frames,stability,Wiener amalgam spaces

O174.2

A

1008-5513(2009)04-0828-05

2008-09-08.

遼寧省科學(xué)技術(shù)基金(002010).

唐青松(1978-),碩士,研究方向：小波分析與信號處理.

張祥德.

2000MSC:42C15