On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms
Nguyen Thanh Hong, Trinh Tuan, Nguyen Xuan Thao (2013)
Applications of Mathematics
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We deal with several classes of integral transformations of the form where is an operator. In case is the identity operator, we obtain several operator properties on with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on and define the inversion formula. Further, for an other class of differential operators...