Wave packet transform in the framework of Lebedev-Skalskaya transforms (Q6548059)

The authors define the wave-packet transform (WPT) involving Lebedev-Skalskaya transform (LS-transform) and study their properties. \par In the first section a discussion on WPT is presented. Then, in the next section basic properties of the continuous LS-transform wavelet are highlighted. \par In the third section, a definition of WPT associated with LS-transform is proposed and several properties (norm inequalities, reconstruction formula, etc,) are presented.\par The Plancherel's and Parseval's relations for WPT associated with LS-transform are the subject of the fourth section and, in the last one, Calderon's reproducing identity using the theory of LS-transform and its associated convolution are discussed.