Generalizing Geometric Nonwindowed Scattering Transforms on Compact Riemannian Manifolds

2024/02/16 by Albert Chua, Yang Yang, Chua, Albert +1
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2402.10771

Abstract

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.

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