One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G, K) is a Gelfand pair, then harmonic analysis on M is closely related to the representations of G and the direct integral decomposition of the space of square-integrable functions on M into irreducible representations of G. The n-dimensional Euclidean space can be realized as the quotient of the orientation preserving Euclidean motion group E(n) by the special orthogonal group SO(n). The pair (E(n),...
One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a gi...