Abstract
We considered convolutions of the generalized H-transforms in Chapter 11. The main property of these convolutions is the following {fy205-1} where (H a f)(x) is the generalized H-transform with the power weight (11.1). It follows from this relation that the H-convolution (f a* )(x) 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 ((1966)–(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.
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© 1994 Springer Science+Business Media Dordrecht
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Yakubovich, S.B., Luchko, Y.F. (1994). Convolutions of Generating Operators. In: The Hypergeometric Approach to Integral Transforms and Convolutions. Mathematics and Its Applications, vol 287. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1196-6_14
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DOI: https://doi.org/10.1007/978-94-011-1196-6_14
Publisher Name: Springer, Dordrecht
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