Wave packet transform and wavelet convolution product involving the index Whittaker transform

The main goal of this paper is to study the wave packet transform (WPT) and wavelet convolution product involving the index Whittaker transform (IWT). Some estimates for the Whittaker wavelet (W-Wavelet) and W-wavelet transform are obtained, and Plancherel’s relation for the WPT-transform is also deduced. Calderón’s formula associated with IWT is obtained. Furthermore, using the convolution property of IWT, the wavelet convolution product is defined, and some related results are discussed.