Conic injectivity sets for the Radon transformation on spheres
The problem under study concerns description of nonzero functions that have zero integrals over all spheres with centers in a given set. For the corresponding integral transformation (Radon transformation on spheres), the kernel is described, and sharp uniqueness theorems are obtained. Applications...
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| Veröffentlicht in: | St. Petersburg mathematical journal 2016-10, Vol.27 (5), p.709-730 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The problem under study concerns description of nonzero functions that have zero integrals over all spheres with centers in a given set. For the corresponding integral transformation (Radon transformation on spheres), the kernel is described, and sharp uniqueness theorems are obtained. Applications of the main results to partial differential equations are considered: new uniqueness theorems are proved for the Darboux equation and the wave equation. |
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| ISSN: | 1061-0022 1547-7371 |
| DOI: | 10.1090/spmj/1413 |