By studying various ways of describing the Narayana triangle, we provide a number of generalizations of this triangle and study some of their properties. In some cases, the diagonal sums of these triangles provide examples of Somos-4 sequences via their Hankel transforms.

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.