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Vol. 48 No. 4 (2022)
Serdica Mathematical Journal

Articles

Generalized pseudo-differential operators associated with symbol classes involving fractional Fourier transform

https://doi.org/10.55630/serdica.2022.48.247-270

Published 15-10-2022

  • Abhisekh Shekhar
    • ,
  • Nawin Kumar Agrawal

Abhisekh Shekhar
C.M.Sc. College

Nawin Kumar Agrawal
Lalit Narayan Mithila University

Abstract

Generalized pseudo-differential operators \(A(x,\Delta'_x)\) and \(\mathcal{A}(x,\Delta'_x)\) involving fractional Fourier transform (FrFT) associated with symbol-classes are defined and respective symbol classes are introduced. Product and commutators of the generalized pseudo-differential operators are investigated.

2020 Mathematics Subject Classification:

35S05, 46E10, 46E35, 46F05, 47G30, 46F12

Keywords

fractional Fourier transform, symbol classes, tempered distribution, pseudo-differential operators, Sobolev space

Full text

Author Details

Abhisekh Shekhar

Department of Mathematics
C.M.Sc. College
Darbhanga(Bihar)-846004, India
e-mail: abhi08.iitkgp@gmail.com

Nawin Kumar Agrawal

University Department of Mathematics
Lalit Narayan Mithila University
Kameshwarnagar, Darbhanga(Bihar)-846004, India
e-mail: drnkumaragrawal@gmail.com

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