An n-dimensional pseudo-differential operator involving the Hankel transformation

作者：Pathak R S^*; Prasad Akhilesh; Kumar Manish

来源：Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2012, 122(1): 99-120.

DOI：10.1007/s12044-012-0050-2

• Hankel transformation
• Hankel convolution
• pseudo-differential operator

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.%26apos;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.

• 出版日期2012-2