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      Permanent link:
      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

       

      R S Pathak1 Akhilesh Prasad2 Manish Kumar2

      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

    • Dates

       
      Published
      February 2012
      Manuscript received
      10 February 2010
      Manuscript revised
      12 November 2011

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