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Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings

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Abstract

We show that compactly supported functions with sufficient smoothness and enough vanishing moments can serve as analyzing vectors for shearlet coorbit spaces. We use this approach to prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone into Besov spaces. Furthermore, we show embedding relations of traces of these subspaces with respect to the real axes.

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Authors and Affiliations

  1. FB12 Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein Straße, Lahnberge, 35032, Marburg, Germany

    Stephan Dahlke

  2. Fachbereich für Mathematik, Technische Universität Kaiserslautern, E. Schrödinger Str., 67653, Kaiserslautern, Germany

    Gabriele Steidl

  3. Institute for Computational Mathematics in Science and Technology, Hochschule Neubrandenburg—University of Applied Sciences, Brodaer Str. 2, 17033, Neubrandenburg, Germany

    Gerd Teschke

Authors
  1. Stephan Dahlke
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  2. Gabriele Steidl
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  3. Gerd Teschke
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Corresponding author

Correspondence to Gabriele Steidl.

Additional information

Communicated by Karlheinz Gröchenig.

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Dahlke, S., Steidl, G. & Teschke, G. Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings. J Fourier Anal Appl 17, 1232–1255 (2011). https://doi.org/10.1007/s00041-011-9181-6

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  • DOI: https://doi.org/10.1007/s00041-011-9181-6

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