Generalizing geometric nonwindowed scattering transforms on compact Riemannian manifolds

We study nonwindowed geometric scattering transforms on compact Riemannian manifolds without boundary. These transforms are formulated as \({\textbf{L}}^q\) ${\mathbf{L}}^q$ -norms, with \(1 < q \le 2\) $1<q\le 2$ , of a cascade of geometric wavelet transforms and modulus operators. We provide weighted measures for these operators, and prove that these operators are well-defined under specific conditions on the manifold, invariant to the action of isometries, and stable to diffeomorphisms for bandlimited functions.