An n-dimensional pseudo-differential operator involving the Hankel transformation |
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| Authors: | R S PATHAK AKHILESH PRASAD MANISH KUMAR |
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| Affiliation: | 1.Centre for Interdisciplinary Mathematical Sciences,Banaras Hindu University,Varanasi,India;2.Department of Applied Mathematics,Indian School of Mines,Dhanbad,India |
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| 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 Hm(In)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. |
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