Generalizing Geometric Nonwindowed Scattering Transforms on Compact Riemannian Manifolds

Let ℳ be a compact, smooth, n-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as 𝐋^q(ℳ) norms of a cascade of geometric wavelet transforms and modulus operators. We then provide weighted measures for these operators, prove that these operators are well-defined under specific conditions on the manifold, invariant to the action of isometries, and stable to diffeomorphisms for λ-bandlimited functions.