Spectral analysis via higher-dimensional shearlet transform

In this paper, we introduce the localization operators associated to the higher-dimensional Shearlet transform HDST introduced earlier in Dahlke et al. (The continuous shearlet transform in arbitrary space dimensions, Philipps-Universität Marburg, (2008), J Fourier Anal Appl 16:340–364, 2010). We prove that they are in the trace class \(S_1\) $S_1$ and we give a trace formula for them. Typical examples of localization operators are presented. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, the second aim of this article is to explore two more aspects of the time-frequency analysis associated with the HDST including the spectral analysis associated with the concentration operators and the scalogram.