Annals of Mathematical Sciences and Applications
Volume 6 (2021)
A pair of Kontorovich–Lebedev type transforms and associated pseudo-differential operators
Pages: 87 – 118
In this paper, we have introduced Kontorovich–Lebedev type transform (KL-type transform) in two variables form, independent of index and further its two classifications are given. Differential operators associated to it is being introduced and further its continuity as well as of KL-type transforms on Zemanian type function spaces are discussed. Moreover, translation and convolution operator involving KL-type transform are given and in Lebesgue space their estimates are deduced. Furthermore, pseudo-differential operators associated to KL-type transforms are defined and on Zemanian type function spaces their continuity has been studied. Ultimately, an application of it has been shown by solving an integral equation.
Kontorovich–Lebedev transform, function spaces, pseudo-differential operator, convolution
2010 Mathematics Subject Classification
35S05, 44A20, 46F12
The second author is supported by Science and Engineering Research Board, Government of India, under Grant No. EMR/2016/005141.
Received 20 October 2020
Accepted 3 February 2021
Published 6 October 2021