Fractional Integrals and Tangency Problems in Integral Geometry
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910766256357376 |
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| author | Rubin, Boris |
| author_facet | Rubin, Boris |
| contents | Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The present article contains new examples of such transforms in the Euclidean, spherical, and hyperbolic settings, when integration is performed over lower-dimensional geodesic spheres or cross-sections, which are tangent to a given surface. Simple inversion formulas are obtained and admissible singularities at the tangency points are studied. Possible applications to the half-ball screening in mathematical tomography and some difficulties related to the general (not necessarily symmetric) case are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional Integrals and Tangency Problems in Integral Geometry Rubin, Boris Functional Analysis 44A12 Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The present article contains new examples of such transforms in the Euclidean, spherical, and hyperbolic settings, when integration is performed over lower-dimensional geodesic spheres or cross-sections, which are tangent to a given surface. Simple inversion formulas are obtained and admissible singularities at the tangency points are studied. Possible applications to the half-ball screening in mathematical tomography and some difficulties related to the general (not necessarily symmetric) case are discussed. |
| title | Fractional Integrals and Tangency Problems in Integral Geometry |
| topic | Functional Analysis 44A12 |
| url | https://arxiv.org/abs/2412.20198 |