A class of index transforms generated by the Mellin and Laplace operators

Classical integral representation of the Mellin type kernel in terms of the Laplace integral gives an idea to construct a new class of non-convolution (index) transforms. Particular examples give the Kontorovich-Lebedev-like transformation and new transformations with hypergeometric functions as kernels. Mapping properties and inversion formulas are obtained. Finally we prove a new inversion theorem for the modified Kontorovich-Lebedev transform

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