Research ArticleNo Access

Two-dimensional $(P, Q)$ -Mellin transform and applications

Pankaj Jain

Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India

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

E-mail Address: pankajkrjain@hotmail.com

Corresponding author.

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Chandrani Basu

Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India

E-mail Address: chandrani.basu@gmail.com

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, and

Vivek Panwar

Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India

E-mail Address: vivek.pan1992@gmail.com

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https://doi.org/10.1142/S1793557122500814Cited by:1 (Source: Crossref)

Abstract

In this paper, we have introduced and studied two-dimensional $(P, Q)$ -Mellin transform which extends the known results of two-dimensional $Q$ -Mellin transform. We provide its several basic properties, the appropriate convolution, the inversion formula and the Parseval-type relations. Some applications of $(P, Q)$ -Mellin transform have been pointed out in solving integral equations. Finally, a Titchmarsh-type theorem has been proved.

Communicated by Lapev

Keywords:

AMSC: 33D05, 33D50, 33D60, 33D90, 44A05, 44A20

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