Traditional methods of time-frequency and multiscale analysis, such as wavelets and Gabor frames, have been successfully employed for representing most classes of pseudodifferential operators. However these methods are not equally effective in dealing with Fourier Integral Operators in general. In this paper, we show that the shearlets, recently introduced by the authors and their collaborators...

In this paper, we study the concept of controlled ∗ -operator frames for space all adjointable operators on a Hilbert id="M4"> C -module H. Also, discuss characterizations id="M5"> and give some properties. Some illustrative examples are provided to advocate usability our results.

We discuss an elementary procedure that allows us to construct dual pairs of wavelet frames based on certain dual pairs of Gabor frames and vice versa. The construction preserves tightness of the involved frames. Starting with Gabor frames generated by characteristic functions the construction leads to a class of tight wavelet frames that include the Shannon (orthonormal) wavelet, and applying ...