Continuity of Pseudo-differential Operators Associated with the Bessel Operator in Some Gevrey Spaces |
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Authors: | R.S. Pathak Akhilesh Prasad |
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Affiliation: | Department of Mathematics , Banaras Hindu University , Varanasi, 221 005, India |
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Abstract: | The pseudo-differential operator (p.d.o) h w , a associated with the Bessel operator d 2 / dx 2 + (1 m 4 w 2 )/4 x 2 involving the symbol a ( x , y ) whose derivatives satisfy certain growth conditions depending on some increasing sequences, is studied on certain Gevrey spaces (ultradifferentiable function spaces). It is shown that the operator h w , a is a continuous linear map of one Gevrey space into another Gevrey space. A special p.d.o. called the Gevrey-Hankel potential is defined and some of its properties are investigated. A variant H w , a of h w , a is also discussed. |
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Keywords: | Pseudo-differential Operator Bessel Operator Hankel Transform Hankel Potential |
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