Abstract Inspired by Jaming’s characterization of the Fourier transform on specific groups via convolution property, we provide a novel approach which characterizes any locally compact abelian group. In particular, our encompasses results. Furthermore, demonstrate that cosine as well Laplace can also be characterized suitable property.

which has the following property Fc(f ∗ g)(x) = (Fcf)(x)(Fcg)(x). (3) The theory of integral transforms related to the Fourier and Mellin convolutions is well developed [2, 6, 10, 11, 12, 13, 19] and has many applications. Some other classes of integral transforms, that are not related to any known convolutions, are considered in [14, 15]. In this paper we investigate integral transforms of the...