Skip to main content
SpringerLink
Log in

Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator

  • Published:
Journal of Pseudo-Differential Operators and Applications Aims and scope Submit manuscript

Abstract

A brief introduction to the fractional Fourier transform and its basic properties is given. Fractional Fourier transform of tempered distributions is studied. Generalized pseudo-differential operators involving two classes of symbols and fractional Fourier transforms are investigated. An application of the fractional Fourier transform in solving a generalized heat equation is 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. Almeida L.B.: The fractional Fourier transform and time–frequency representations. IEEE Trans. Signal Process. 42(11), 3084–3091 (1994)

    Article  Google Scholar 

  2. Bhosale B.N., Chaudhary M.S.: Fractional Fourier transform of distributions of compact support. Bull. Cal. Math. Soc. 94(5), 349–358 (2002)

    MathSciNet  MATH  Google Scholar 

  3. Pathak R.S.: A Course in Distribution Theory and Applications. Narosa Publishing House, New Delhi (2009)

    Google Scholar 

  4. Prasad A., Kumar M.: Product of two generalized pseudo-differential operators involving fractional Fourier transform. J. Pseudo Differ. Oper. Appl. 2(3), 355–365 (2011)

    Article  MathSciNet  Google Scholar 

  5. Zaidman, S.: Distributions and Pseudo-differential Operators. Longman, Essex., England (1991)

  6. Zayed A.I.: Fractional Fourier transform of generalized functions. Integr. Transform. Spec. Funct. 7(3–4), 299–312 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, 221005, India

    R. S. Pathak

  2. Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, India

    Akhilesh Prasad & Manish Kumar

Authors
  1. R. S. Pathak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akhilesh Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manish Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manish Kumar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pathak, R.S., Prasad, A. & Kumar, M. Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator. J. Pseudo-Differ. Oper. Appl. 3, 239–254 (2012). https://doi.org/10.1007/s11868-012-0047-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11868-012-0047-8

Keywords

Mathematics Subject Classification (2000)

Search

Navigation