Spectral analysis via higher-dimensional shearlet transform

In this paper, we introduce the localization operators associated to the higherdimensional 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 S1 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