Research ArticleNo Access

Pseudo-differential operator in the framework of linear canonical transform domain

Akhilesh Prasad

Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India

E-mail Address: apr_bhu@yahoo.com

Corresponding author.

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Z. A. Ansari

Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India

E-mail Address: alzamir.ansari@gmail.com

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, and

Pankaj Jain

Department of Mathematics, South Asian University, New Delhi 110021, India

E-mail Address: pankaj.jain@sau.ac.in

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https://doi.org/10.1142/S1793557121501175Cited by:5 (Source: Crossref)

Abstract

The main goal of this paper is to study properties of the linear canonical transform (LCT) on Schwartz-type space $𝒮_{A} (ℝ)$ . The symbol class $𝒮_{ρ, σ}^{m, A}$ is introduced. The pseudo-differential operator (p.d.o.) involving LCT is defined and also some of its properties including boundedness are investigated in Sobolev-type space. Kernel and integral representation of p.d.o. are obtained. Some applications of LCT to generalized partial differential equations and canonical convolution integral equation have been solved.

Communicated by N. C. Wong

Keywords:

AMSC: 46F12, 43A32, 46F05, 47G30, 35S05, 53D22, 46E35

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