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Wavelet convolution product involving fractional fourier transform

  • S. K. Upadhyay EMAIL logo und Jitendra Kumar Dubey
Veröffentlicht/Copyright: 19. Februar 2017
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Fractional Calculus and Applied Analysis
Aus der Zeitschrift Fractional Calculus and Applied Analysis Band 20 Heft 1

Abstract

Exploiting the theory of fractional Fourier transform, the wavelet convolution product and existence theorems associated with the n-dimensional wavelet transform are investigated and their properties studied.

Key Words and Phrases: wavelet transform; wavelet convolution; generalized convolution; fractional Fourier transform
MSC 2010: 42A38; 42C40; 44A35

Acknowledgements

The first author is thankful to IIT(BHU) and DST-Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, India, for providing research facilities. The second author is thankful to DST-Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, India, for providing research facilities.

References

[1] C.K. Chui, An Introduction to Wavelets. Academic Press, New York (1992).10.1063/1.4823126Suche in Google Scholar

[2] Y. Meyer, Wavelets and Operators. Cambridge University Press (1992).10.1017/CBO9780511623820Suche in Google Scholar

[3] T. Morita and K. Sato, Molification of fractional derivatives using rapidly decaying harmonic wavelet. Fract. Calc. Appl. Anal. 14, No 2 (2011), 284–300; DOI: 10.2478/s13540-011-0017-5; https://www.degruyter.com/view/j/fca.2011.14.issue-2/issue-files/fca.2011.14.issue-2.xml.10.2478/s13540-011-0017-5;Suche in Google Scholar

[4] R.S. Pathak, The Wavelet Transform. Atlantis Press, World Scientific (2009).10.2991/978-94-91216-24-4Suche in Google Scholar

[5] R.S. Pathak, The Wavelet convolution product. Investigations in Mathematical Sciences4 (2014), 101–113.10.2991/978-94-91216-24-4_8Suche in Google Scholar

[6] N.X. Thao, V.K. Tuan and N.T. Hong, A Fourier generalized convolution transform and applications to integral equations. Fract. Calc. Appl. Anal. 15, No 3 (2012), 493–508; DOI: 10.2478/s13540-012-0035-y; https://www.degruyter.com/view/j/fca.2012.15.issue-3/issue-files/fca.2012.15.issue-3.xml.10.2478/s13540-012-0035-y;Suche in Google Scholar

[7] S.K. Upadhyay and J.K. Dubey, Pseudo-differential operators of infinite order on WMΩ(Cn)-space involving fractional Fourier transform. J. Pseudo-Differ. Oper. Appl. 6 (2015), 113–133.10.1007/s11868-014-0105-5Suche in Google Scholar

[8] S.K. Upadhyay, A. Kumar and J.K. Dubey, Characterization of spaces of type W and pseudo-differential operators of infinite order involving fractional Fourier transform. J. Pseudo-Differ. Oper. Appl. 5 (2014), 215–230.10.1007/s11868-014-0092-6Suche in Google Scholar

[9] A.I. Zayed, A convolution and product theorem for the fractional Fourier transform. IEEE Signal Proc. Letters5 (1998), 101–103.10.1109/97.664179Suche in Google Scholar

Received: 2015-11-23
Revised: 2016-10-26
Published Online: 2017-2-19
Published in Print: 2017-2-1

© 2017 Diogenes Co., Sofia

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 20–1–2017)
  4. Survey paper
  5. Ten equivalent definitions of the fractional laplace operator
  6. Research paper
  7. Consensus of fractional-order multi-agent systems with input time delay
  8. Research paper
  9. Asymptotic behavior of solutions of nonlinear fractional differential equations with Caputo-Type Hadamard derivatives
  10. Research paper
  11. A preconditioned fast finite difference method for space-time fractional partial differential equations
  12. Research paper
  13. On existence and uniqueness of solutions for semilinear fractional wave equations
  14. Research paper
  15. Computational solutions of the tempered fractional wave-diffusion equation
  16. Research paper
  17. Completeness on the stability criterion of fractional order LTI systems
  18. Research paper
  19. Wavelet convolution product involving fractional fourier transform
  20. Research paper
  21. Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method
  22. Research paper
  23. A foundational approach to the Lie theory for fractional order partial differential equations
  24. Research paper
  25. Null-controllability of a fractional order diffusion equation
  26. Research paper
  27. New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions
  28. Research paper
  29. The stretched exponential behavior and its underlying dynamics. The phenomenological approach
  30. Short Paper
  31. Lyapunov-type inequality for an anti-periodic fractional boundary value problem
https://doi.org/10.1515/fca-2017-0009
Schlagwörter für diesen Artikel
wavelet transform; wavelet convolution; generalized convolution; fractional Fourier transform

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA–volume 20–1–2017)
  4. Survey paper
  5. Ten equivalent definitions of the fractional laplace operator
  6. Research paper
  7. Consensus of fractional-order multi-agent systems with input time delay
  8. Research paper
  9. Asymptotic behavior of solutions of nonlinear fractional differential equations with Caputo-Type Hadamard derivatives
  10. Research paper
  11. A preconditioned fast finite difference method for space-time fractional partial differential equations
  12. Research paper
  13. On existence and uniqueness of solutions for semilinear fractional wave equations
  14. Research paper
  15. Computational solutions of the tempered fractional wave-diffusion equation
  16. Research paper
  17. Completeness on the stability criterion of fractional order LTI systems
  18. Research paper
  19. Wavelet convolution product involving fractional fourier transform
  20. Research paper
  21. Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method
  22. Research paper
  23. A foundational approach to the Lie theory for fractional order partial differential equations
  24. Research paper
  25. Null-controllability of a fractional order diffusion equation
  26. Research paper
  27. New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions
  28. Research paper
  29. The stretched exponential behavior and its underlying dynamics. The phenomenological approach
  30. Short Paper
  31. Lyapunov-type inequality for an anti-periodic fractional boundary value problem
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