MELLIN TRANSFORM AS PARTICULAR REALIZATION OF GENERAL SCHEME OF INTEGRAL TRANSFORM CONSTRUCTION

Abstract

The paper is to study application of a general scheme pertaining to integral transform construction with the purpose to obtain the well-known Mellin transform.A determining factor of its construction is a linear differential operator T = t d/dt in the {f(0)}. «originals» set. The paper shows that in the case of a linear algebraic operator the simplest and agreed-upon transform is obtained with the help of multiplication of the corresponding F(u) «image» by a trivial k(u) = –и function.