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<p>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 survey suggests 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. Potential application to the half-ball screening in mathematical tomography and some open problems are discussed.</p>

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TANGENCY PROBLEMS IN INTEGRAL GEOMETRY AND FRACTIONAL INTEGRALS

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Boris Rubin

摘要

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 survey suggests 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. Potential application to the half-ball screening in mathematical tomography and some open problems are discussed.