caa a22 4500 445868805 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00605-010-0264-2 doi (NATIONALLICENCE)springer-10.1007/s00605-010-0264-2 Grohs Philipp ETH Zürich, Seminar of Applied Mathematics, Rämistraße 101, 8092, Zürich, Switzerland aut Continuous shearlet frames and resolution of the wavefront set [Elektronische Daten] [Philipp Grohs] In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are—unlike more traditional transforms like wavelets—able to efficiently handle data with features along edges. The main result in Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719-2754, 2009) confirming this property for shearlets is due to Kutyniok and Labate where it is shown that for very special functions ψ with frequency support in a compact conical wegde the decay rate of the shearlet coefficients of a tempered distribution f with respect to the shearlet ψ can resolve the wavefront set of f. We demonstrate that the same result can be verified under much weaker assumptions on ψ, namely to possess sufficiently many anisotropic vanishing moments. We also show how to build frames for $${L^2(\mathbb{R}^2)}$$ from any such function. To prove our statements we develop a new approach based on an adaption of the Radon transform to the shearlet structure. Springer-Verlag, 2010 Wavefront set nationallicence Continuous frames nationallicence Shearlets nationallicence Microlocal analysis nationallicence Monatshefte für Mathematik Springer Vienna 164/4(2011-12-01), 393-426 0026-9255 164:4<393 2011 164 605 https://doi.org/10.1007/s00605-010-0264-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0264-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Grohs Philipp ETH Zürich, Seminar of Applied Mathematics, Rämistraße 101, 8092, Zürich, Switzerland aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/4(2011-12-01), 393-426 0026-9255 164:4<393 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer