Wavelet transforms associated with the Index Whittaker transform
Ashish Pathak, Abhishek
TL;DR
This paper explores the properties of the continuous and discrete Index Whittaker wavelet transforms, including boundedness, Plancherel, and reconstruction formulas, advancing the theoretical understanding of this transform family.
Contribution
It introduces the continuous and discrete Index Whittaker wavelet transforms and establishes their fundamental properties and formulas.
Findings
Boundedness of the transforms
Plancherel formula derived
Reconstruction formula established
Abstract
In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as reconstruction formula for the continuous Index Whittaker Wavelet Transform (CIWWT) are obtain and Finally we discuss the discrete version of index Whittaker wavelet transform.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Nonlinear Waves and Solitons · Image and Signal Denoising Methods