Extended ridgelet transform on distributions and Boehmians (Q2891031)

Since the ridgelet transform represents very high directional sensitivity and simultaneously highly anisotropic, it outperforms the wavelet transform which does not possess these characteristics (however, in the wavelet transform there is only a fixed number of directional elements), see [\textit{J. L. Strack} et al., Astronom. Astrophys. 398, 785--800 (2003)]. This and other similar splendid properties of the ridgelet transform initiated a lot of research in the recent past and ever since its christening by \textit{E. J. Candès}, see [Appl. Comput. Harmon. Anal. 6, No. 2, 197--218 (1999; Zbl 0931.68104)] and references given in this paper under review. Interestingly, the author could, in this paper, extend his own work from 2010.NEWLINENEWLINEThe paper can be thought of as consisting of two sections, in the first one, the ridgelet transform is extended to the Schwartz distribution space that contains the space of tempered distributions, where none of the (above mentioned) spaces contains the space of tempered Boehmians nor is contained in it. In the second section, the ridgelet transforms are extended to the space of \(C^\infty\)-Boehmians, which removes the above mentioned drawbacks.