Shearlet coorbit spaces and associated Banach frames

Dahlke, Stephan; Kutyniok, Gitta ; Steidl, Gabriele und Teschke, Gerd (2009): Shearlet coorbit spaces and associated Banach frames. In: Applied and Computational Harmonic Analysis, Vol. 27, No. 2: pp. 195-214

Abstract

In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 10635203
• Language: English