Generalizing Geometric Nonwindowed Scattering Transforms on Compact Riemannian Manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911778453061632 |
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| author | Chua, Albert Yang, Yang |
| author_facet | Chua, Albert Yang, Yang |
| contents | Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalizing Geometric Nonwindowed Scattering Transforms on Compact Riemannian Manifolds Chua, Albert Yang, Yang Functional Analysis Classical Analysis and ODEs Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ 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. |
| title | Generalizing Geometric Nonwindowed Scattering Transforms on Compact Riemannian Manifolds |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2402.10771 |