Coorbit Spaces with Voice in a Fréchet Space

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• 作者：S. Dahlke ; F. De Mari ; E. De Vito ; D. Labate…
• 关键词：Coorbit spaces ; Fréchet spaces ; Representations of locally compact groups ; Reproducing formulae
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：23
• 期：1
• 页码：141-206
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics;
• 出版者：Springer US
• ISSN：1531-5851
• 卷排序：23

文摘

We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group G that are not necessarily irreducible nor integrable. Our basic assumption is that the kernel associated with the voice transform belongs to a Fréchet space \(\mathcal T\) of functions on G, which generalizes the classical choice \(\mathcal T=L_w^1(G)\). Our basic example is \( \mathcal T=\bigcap _{p\in (1,+\infty )} L^p(G)\), or a weighted versions of it. By means of this choice it is possible to treat, for instance, Paley-Wiener spaces and coorbit spaces related to Shannon wavelets and Schrödingerlets.