Abstract
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.
| Original language | English |
|---|---|
| Journal | Journal of Mathematical Sciences (United States) |
| DOIs | |
| State | Accepted/In press - 2026 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2026.
Keywords
- Fractional integrals
- Hyperbolic slices
- Spherical means
- Tangent chords
- Tangent spheres
Fingerprint
Dive into the research topics of 'TANGENCY PROBLEMS IN INTEGRAL GEOMETRY AND FRACTIONAL INTEGRALS'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver