Certain integral transforms with the Macdonald function Kν(z) in the kernels

Four integral transforms are considered with the Macdonald function in their kernels. Existence and inversion theorems are proved and Parseval equalities are established in a Hilbert space, in a Wiener normed ring, and in the space of generalized Gelfand-Shilov functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 990–993, July, 1990.