The Continuous Fractional Wavelet Transform on W-Type Spaces

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Authors

  • Anuj Kumar
     Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University). Varanasi - 221005 ,IN
  • S. K. Upadhyay
     DST-CIMS, Department of Mathematical Sciences, Indian Institute of Technol- ogy (Banaras Hindu University), Varanasi - 221005 ,IN

DOI:

https://doi.org/10.18311/jims/2018/20984

Keywords:

Fractional Fourier Transform, Fractional Wavelet Transform, Convex Functions, Gel'fand and Shilov Spaces
Stoichiometry

Abstract

An n-dimensional continuous fractional wavelet transform involving n-dimensional fractional Fourier transform is studied and its properties are obtained on Gel'fand and Shilov spaces of type WM(Rn), WΩ (Cn) and WΩM (Cn). It is shown that continuous fractional wavelet transform, WαψΦ : WM(Rn) → WM(Rn í— R+), WαψΦ : WΩ (Cn) → WΩ (Cn í— R+) and WαψΦ : WΩM (Cn) → WΩM (Cn í— R+) are linear and continuous maps, where Rn and Cn are the usual Euclidean spaces.

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Published

2018-06-01

How to Cite

Kumar, A., & Upadhyay, S. K. (2018). The Continuous Fractional Wavelet Transform on W-Type Spaces. The Journal of the Indian Mathematical Society, 85(3-4), 377–395. https://doi.org/10.18311/jims/2018/20984

Issue

Volume 85, Issue 3-4, July-December 2018

Section

Articles

License

Copyright (c) 2018 Anuj Kumar, S. K. Upadhyay

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2018-04-25
Accepted 2018-04-25
Published 2018-06-01

 

References

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