Characterization of Product of Pseudo-Differential Operators Involving Fractional Fourier Transform

Jump To References Section

Authors

  • Department of Mathematics, Galgotias University, Greater Noida, 226001 ,IN
  • Department of Mathematics, DCSK P. G. College, Mau - 275101 ,IN
  • Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi - 221005 ,IN

DOI:

https://doi.org/10.18311/jims/2021/26085

Keywords:

Fractional Fourier transform, Pseudo-differential operator, Adjoint operator

Abstract

Characterizations of product of generalized pseudo-differential operators associated with symbol σ(x,ξ) ∈ Sm are discussed by exploiting the fractional Fourier transform.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

2021-01-28

How to Cite

Kumar Dubey, J., Kumar Pandey, P., & Upadhyay, S. K. (2021). Characterization of Product of Pseudo-Differential Operators Involving Fractional Fourier Transform. The Journal of the Indian Mathematical Society, 88(1-2), 60–71. https://doi.org/10.18311/jims/2021/26085
Received 2020-09-18
Accepted 2023-01-30
Published 2021-01-28

 

References

Z. L. Abzhandadze and V. F. Osipov, Fourier-Fresnel Transform and Some of its Applications, Univ. of Saint-Petersbourg, 2000.

E. Cordero and K. Grochenig, On the product of localization Operators, in: Modern Trends in Pseudo-differential Operators, pp. 279295, Oper. Theory Adv. Appl., Vol. 172, Birkhuser, Basel, 2007.

J. Du and M. W. Wong, A product formula for localization operators, Bull. Korean Math. Soc. 37 (2000), 77-84 .

J. K. Dubey, A. Kumar and S. K. Upadhyay, Pseudo-differential operators and Localization operators on Sμv (R) space involving fractional Fourier transform, Novi Sad J. Math., 45(2015), 285–301.

K. Gr¨ochenig, Composition and spectral invariance of pseudo-differential operators on modulation space, J. Anal. Math. 98 (2006), 65–82.

H. M. Ozaktas, M. A. Kutay and Z. Zalevsky, The Fractional Fourier Transform with Applications in Optics and Signal Processing, John Wiley and Sons, New York, 2000.

R. S. Pathak and A. Prasad, A generalized pseudo-differential operator on GelfandShilov space and Sobolev space, Indian J. Pure Appl. Math. 37 (2006), 223–235.

J. Sjostrand, An algebra of pseudo-differential Operators, Math. Res. Lett. 1 (1994), 185-192.

S. K. Upadhyay and J. K. Dubey, Pseudo-Differential Operators of infinite order on WΩM (Cn)- spaces involving fractional Fourier transform, J. Pseudo-Differ. Oper. Appl. 6 (2015), 113–133.

M. W. Wong, An Introduction to Pseudo-differential Operators, 3rd edn., World Scientific, Singapore, 2014.