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GENERALIZED PSEUDO-DIFFERENTIAL OPERATORS INVOLVING FRACTIONAL FOURIER TRANSFORM

  • Waphare, B.B. (Commerce and Science College) ;
  • Pansare, P.D. (Savitribai Phule Pune University)
  • Received : 2020.08.03
  • Accepted : 2021.02.05
  • Published : 2021.03.15

Abstract

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

Keywords

References

  1. L. Almeida, The fractional Fourier transform and time frequency representations, IEEE Trans. Signal Process, 42(11) (1994), 3084-3091. https://doi.org/10.1109/78.330368
  2. R.S. Pathak and A. Prasad, A generalized pseudo-differential operator on Gelfand-Shilov space and Sobolev space, Indian J. Pure Appl. Math., 37(4) (2006), 223-235.
  3. M.W. Wong, An Introduction to pseudo-differential operators, 2nd edition, World Scientific, Sinfapore, (1999).
  4. S. Zaidman, Distributions and pseudo-differential operators, Longman, Essex, England (1991).
  5. A.I. Zayed, A convolution and product theorem for the fractional Fourier transform, IEEE Signal Process. Lett., 5(4) (1998), 101-103.
  6. A.I. Zayed, Fractional Fourier transform of generalized functions, Integral transforms Spec. Funct., 7(3-4) (1998), 299-312. https://doi.org/10.1080/10652469808819206