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.

中文翻译：

---

与索引 Whittaker 变换相关的小波变换

使用其卷积理论定义和讨论了与索引 Whittaker 变换相关的连续小波变换 (CWT)。得到了CWT的存在定理和重构公式。此外，讨论了CWT的组成，并推导出其Plancherel和Parseval的关系。进一步给出了该小波变换的离散形式及其重构公式。此外，还讨论了离散惠特克小波变换的某些性质。