Wavelet transforms associated with the index Whittaker transform

The continuous wavelet transform (CWT) associated with the index Whittaker transform is defined and discussed using its convolution theory. Existence theorem and reconstruction formula for CWT are obtained. Moreover, composition of CWT is discussed, and its Plancherel's and Parseval's relations are also derived. Further, the discrete version of this wavelet transform and its reconstruction formula are given. Furthermore, certain properties of the discrete Whittaker wavelet transform are discussed.

Automated summary

This paper discusses the relationship between the continuous wavelet transform and the Whittaker transform, including the existence theorem, reconstruction formula, composition, Plancherel's and Parseval's relations, as well as the properties of the discrete version and its reconstruction formula.