Banach frames for α-modulation spaces
- 作者：Massimo Fornasier
- 关键词：Banach frames ; Gabor analysis ; Localization of frames ; α ; -modulation spaces ; wavelets
- 刊名：Applied and Computational Harmonic Analysis
- 出版年：2007
- 期刊代码：119_10635203
- 类别：cp
- 出版时间：March 2007
- 卷：22
- 期：2
- 页码：157-175
- 文件大小：266 K
摘要
This paper is concerned with the characterization of α-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation and dilation of a mother atom. In particular, the parameter α[0,1] governs the dependence of the dilation factor on the frequency. The result is achieved by exploiting intrinsic properties of localization of such frames. The well-known Gabor and wavelet frames arise as special cases (α=0) and limiting case (α→1), to characterize respectively modulation and Besov spaces. This intermediate theory contributes to a further answer to the theoretical need of a common interpretation and framework between Gabor and wavelet theory and to the construction of new tools for applications in time–frequency analysis, signal processing, and numerical analysis.