The Hypergeometric Approach to Integral Transforms and Convolutions, Mathematics and its Applications 287, S.B. Yakubovich and Yu F. Luchko, Kluwer Academic, Dordrecht, 1994, xi + 324 pp (original) (raw)

We considered convolutions of the generalized H-transforms in Chapter 11. The main property of these convolutions (f : g)(:c) is the following where (H"f)(:c) is the generalized H-transform with the power weight (11.1). It follows from this relation that the H-convolution (f: g)(:c) is connected with some integral transform and this connection is reflected in the names of other convolutions (Laplace convolution, Mellin convolution, et c.). A different approach to the definition of convolution, which connects some other operator with a convolution has been proposed by I.H.Dimovski «1966I.H.Dimovski « )-(1981))). His definition is more suitable in developing a Mikusinski type operational calculus. In this chapter we will deal with convolutions in the Dimovski's sense.