Skip to main content
SpringerLink
Log in

Calderon’s reproducing formula for Watson wavelet transform

  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper the inverse Watson wavelet transform is investigated, the Calderon reproducing formula of Watson convolution is obtained by generalizing the results of [6]. Some applications associated with Calderon’s reproducing formula of Watson convolution are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. J. Betancor and B. J. Gonzalez, A convolution operation for a distributional Hankel transformation, Studia Mathematica, 117(1) (1985), 57–72.

    MathSciNet  Google Scholar 

  2. L. Debnath, Integral transforms and their applications, CRC Press, New York (1995).

    MATH  Google Scholar 

  3. A. Erdelyi, Higher Transcendental functions vol. 1, Mc-Graw-Hill, New York (1953).

    Google Scholar 

  4. A. Erdelyi, Tables of Integral Transforms vol.1., Mc-Graw-Hill, New York (1954).

    Google Scholar 

  5. E. Lieb and M. Loss, Analysis, 2nd edition, American Mathematical Society Providence Rhode Island (2001).

    MATH  Google Scholar 

  6. M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and the study of function spaces, CBMS Regional Conference series in Mathematics, Vol. 79, American Mathematical Society, Rhode Island, (1991).

    MATH  Google Scholar 

  7. Roop Narain, The G-function as unsymmetrical Fourier Kernels II, Proc. Amer. Math. Soc., 14 (1963), 18–28.

    MATH  MathSciNet  Google Scholar 

  8. R. S. Pathak and G. Pandey, Calderon’s Reproducing Formula For Hankel convolution, International Journal of Mathematics and Mathematical Sciences, 2006 (2006), 1–7.

    Article  MathSciNet  Google Scholar 

  9. R. S. Pathak and S. Tiwari, Pseudo differential operators involving Watson transform, Appl Anal., 86(10) (2007), 1223–1236.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. S. Pathak and S. Tiwari, Watson convolution operator, Prog. of Maths, 40(1&2) (2006), 57–75.

    MATH  MathSciNet  Google Scholar 

  11. R. S. Pathak, A theorem of Hardy and Titchmarsh for Generalized Functions, Appl Anal, 18 (1984), 245–255.

    Article  MATH  Google Scholar 

  12. E. C. Titchmarsh, Introduction to the Theory of Fourier integrals, 2nd edition, Oxford University press, Oxford, U.K. (1948).

    Google Scholar 

  13. S. K. Upadhyay and Alok Tripathi, Continuous Watson wavelet transform, Integr Transf Spec F, 23(9) (2012), 639–647.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DST-CIMS, Department of Applied Mathematics, Indian Institute of Technology, Banaras Hindu University, Varanasi, 221 005, India

    S. K. Upadhyay

  2. Department of Applied Mathematics, Indian Institute of Technology, Banaras Hindu University, Varanasi, 221 005, India

    Alok Tripathi

Authors
  1. S. K. Upadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alok Tripathi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. K. Upadhyay.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Upadhyay, S.K., Tripathi, A. Calderon’s reproducing formula for Watson wavelet transform. Indian J Pure Appl Math 46, 269–277 (2015). https://doi.org/10.1007/s13226-015-0137-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-015-0137-4

Key words

Search

Navigation