# Wavelet transforms associated with the index Whittaker transform

@article{Prasad2021WaveletTA, title={Wavelet transforms associated with the index Whittaker transform}, author={Akhilesh Prasad and Jeetendrasingh Maan and Sandeep Kumar Verma}, journal={Mathematical Methods in the Applied Sciences}, year={2021}, volume={44}, pages={10734 - 10752} }

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…

## One Citation

### Weyl operator associated with index Whittaker transform

- MathematicsJournal of Pseudo-Differential Operators and Applications
- 2022

## References

SHOWING 1-10 OF 50 REFERENCES

### Wavelet transforms associated with the Kontorovich-Lebedev transform

- MathematicsInt. J. Wavelets Multiresolution Inf. Process.
- 2017

The main objective of this paper is to study continuous wavelet transform (CWT) using the convolution theory of Kontorovich–Lebedev transform (KL-transform) and discuss some of its basic properties.…

### Continuous wavelet transform associated with zero-order Mehler-Fock transform and its composition

- MathematicsInt. J. Wavelets Multiresolution Inf. Process.
- 2018

Time-invariant filter has been defined and proved convolution operator and wavelet transform are represented as time-Invariant transform.

### The generalized continuous wavelet transform associated with the fractional Fourier transform

- MathematicsJ. Comput. Appl. Math.
- 2014

### A certain family of fractional wavelet transformations

- MathematicsMathematical Methods in the Applied Sciences
- 2019

In the present paper, a fractional wavelet transform of real order α is introduced, and various useful properties and results are derived for it. These include (for example) Perseval's formula and…

### Composition of the Continuous Fractional Wavelet Transforms

- Mathematics
- 2016

The main goal of this paper is to study the composition of continuous fractional wavelet transform (CFrWT) and its some boundedness results on generalized weighted Sobolev spaces. Application of the…

### Laguerre wavelet transforms

- Computer Science
- 2009

Using convolution theory of the Laguerre transform, Laguerre wavelet transform (LWT) is defined. Certain boundedness results and reconstruction formula for the continuous LWT are obtained. A discrete…

### Continuous Wavelet Transform of Schwartz Tempered Distributions in S′ ( R n )

- MathematicsSymmetry
- 2019

It turns out that the wavelet transform of a constant distribution is zero and the corresponding wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of aNon- constant distribution with a non non-zero constant distribution.

### On the product formula and convolution associated with the index Whittaker transform

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

### A novel fractional wavelet transform and its applications

- Engineering
- 2012

The wavelet transform (WT) and the fractional Fourier transform (FRFT) are powerful tools for many applications in the field of signal processing. However, the signal analysis capability of the…