The pseudodifferential operator A ( x, D )

R. S. Pathak and S. Pathak

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-13

Abstract:

The pseudodifferential operator (p.d.o.) A ( x , D ) , associated with the Bessel operator d 2 / d x 2 + ( 1 − 4 μ 2 ) / 4 x 2 , is defined. Symbol class H ρ , δ m is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space H μ into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution L σ , α p -norm continuity of the p.d.o. is proved.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:848506

DOI: 10.1155/S0161171204212388

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