Cesàro summability of Hölder functions and Talbot effect on rank one Riemannian symmetric spaces of compact type
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915910387761152 |
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| author | Dewan, Utsav |
| author_facet | Dewan, Utsav |
| contents | On rank one Riemannian symmetric spaces of compact type (of dimension $\ge 2$), we first obtain a quantitative characterization of Hölder continuity in terms of Cesàro means. In addition to some approximation theoretic applications, we also apply it to study the celebrated physical phenomenon known as `Talbot effect' arising from diffraction theory. More precisely, for almost every fixed time instance, we study the Hölder continuity and the fractal profile of the Schrödinger propagation in terms of the decay of the Littlewood-Paley projections of the initial data. In the process, we also obtain oscillatory expansions of zonal spherical functions uniformly near the origin and near the cut locus respectively, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02305 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cesàro summability of Hölder functions and Talbot effect on rank one Riemannian symmetric spaces of compact type Dewan, Utsav Classical Analysis and ODEs Analysis of PDEs Primary 43A85, 22E30, Secondary 42B08, 43A55, 28A80 On rank one Riemannian symmetric spaces of compact type (of dimension $\ge 2$), we first obtain a quantitative characterization of Hölder continuity in terms of Cesàro means. In addition to some approximation theoretic applications, we also apply it to study the celebrated physical phenomenon known as `Talbot effect' arising from diffraction theory. More precisely, for almost every fixed time instance, we study the Hölder continuity and the fractal profile of the Schrödinger propagation in terms of the decay of the Littlewood-Paley projections of the initial data. In the process, we also obtain oscillatory expansions of zonal spherical functions uniformly near the origin and near the cut locus respectively, which may be of independent interest. |
| title | Cesàro summability of Hölder functions and Talbot effect on rank one Riemannian symmetric spaces of compact type |
| topic | Classical Analysis and ODEs Analysis of PDEs Primary 43A85, 22E30, Secondary 42B08, 43A55, 28A80 |
| url | https://arxiv.org/abs/2604.02305 |