The Pseudo-differential Operator hmu,a on Hankel Invariant Spaces

Authors: Pathak R.S.1; Prasad A.1

Source: Applicable Analysis, Volume 82, Number 2, 2003 , pp. 187-196(10)

Publisher: Taylor and Francis Ltd

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Abstract:

Using Hankel transform the symbol 'a' is defined and the pseudo-differential operator (p.d.o.) hmu,a associated with the Bessel operator d2 / dx2 + (1 - 4mu 2) / 4x2 in terms of this symbol is defined. It is shown that the operator hmu,a is a continuous linear map of a Hankel invariant space into itself. A special pseudo-differential operator called the Hankel potential is defined and some of its properties are investigated.

Keywords: Hankel transform; Pseudo-differential operator; Bessel operator; Hankel invariant space; Hankel potential

Document Type: Research article

DOI: 10.1080/000368103763297465

Affiliations: 1: Department of Mathematics, Banaras Hindu University Varanasi - 221 005, India

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