Surjectivity of convolution operators on harmonic $NA$ groups
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912078345797632 |
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| author | Papageorgiou, Effie |
| author_facet | Papageorgiou, Effie |
| contents | Let $μ$ be a radial compactly supported distribution on a harmonic $NA$ group. We prove that the right convolution operator $c_μ:f \mapsto f* μ$ maps the space of smooth $\mathfrak{v}$-radial functions onto itself if and only if the spherical Fourier transform $\widetildeμ(λ)$, $λ\in \mathbb{C}$, is slowly decreasing. As an application, we prove that certain averages over spheres are surjective on the space of smooth $\mathfrak{v}$-radial functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Surjectivity of convolution operators on harmonic $NA$ groups Papageorgiou, Effie Functional Analysis 43A85, 43A90, 22E30 Let $μ$ be a radial compactly supported distribution on a harmonic $NA$ group. We prove that the right convolution operator $c_μ:f \mapsto f* μ$ maps the space of smooth $\mathfrak{v}$-radial functions onto itself if and only if the spherical Fourier transform $\widetildeμ(λ)$, $λ\in \mathbb{C}$, is slowly decreasing. As an application, we prove that certain averages over spheres are surjective on the space of smooth $\mathfrak{v}$-radial functions. |
| title | Surjectivity of convolution operators on harmonic $NA$ groups |
| topic | Functional Analysis 43A85, 43A90, 22E30 |
| url | https://arxiv.org/abs/2410.15043 |