Inverses of Product Kernels and Flag Kernels on Graded Lie Groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911682098364416 |
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| author | Stokolosa, Amelia |
| author_facet | Stokolosa, Amelia |
| contents | Let $T(f) = f * K$, where $K$ is a product kernel or a flag kernel on a direct product of graded Lie groups $G= G_1 \times \cdots \times G_ν$. Suppose $T$ is invertible on $L^2(G)$. We prove that its inverse is given by $T^{-1}(g) = g*L$, where $L$ is a product kernel or a flag kernel accordingly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00914 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inverses of Product Kernels and Flag Kernels on Graded Lie Groups Stokolosa, Amelia Classical Analysis and ODEs 42B20 (Primary), 42B35, 42B37, 43A85 (Secondary) Let $T(f) = f * K$, where $K$ is a product kernel or a flag kernel on a direct product of graded Lie groups $G= G_1 \times \cdots \times G_ν$. Suppose $T$ is invertible on $L^2(G)$. We prove that its inverse is given by $T^{-1}(g) = g*L$, where $L$ is a product kernel or a flag kernel accordingly. |
| title | Inverses of Product Kernels and Flag Kernels on Graded Lie Groups |
| topic | Classical Analysis and ODEs 42B20 (Primary), 42B35, 42B37, 43A85 (Secondary) |
| url | https://arxiv.org/abs/2305.00914 |