Abstract
ABSTRACTWe deal with several classes of integral transformations of the formwhere D is a special differential operator. In case D is the identical operator, we prove a Young type theorem for a generalized convolution operator related to the Fourier and the Kontorovich–Lebedev integral transforms. In case D is a certain finite order differential operator, we study the unitary property of these transforms and apply them to solve a class of integro-differential equations. Several classes of system of integral equations are also considered.
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