• An 𝑛-Dimensional Pseudo-Differential Operator Involving the Hankel Transformation

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/122/01/0099-0120

• Keywords

Hankel transformation; Hankel convolution; pseudo-differential operator.

• Abstract

An 𝑛-dimensional pseudo-differential operator (p.d.o.) involving the 𝑛-dimensional Hankel transformation is defined. The symbol class $H^m$ is introduced. It is shown that p.d.o.'s associated with symbols belonging to this class are continuous linear mappings of the 𝑛-dimensional Zemanian space $H_\mu(I^n)$ into itself. An integral representation for the p.d.o. is obtained. Using the Hankel convolution, it is shown that the p.d.o. satisfies a certain $L^1$-norm inequality.

• Author Affiliations

1. Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi 221 005, India
2. Department of AppliedMathematics, Indian School of Mines, Dhanbad 826 004, India

• Proceedings – Mathematical Sciences

Volume 130, 2020
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Posted on July 25, 2019