Fractional Integrals and Tangency Problems in Integral Geometry

Autor:	Rubin, Boris
Rok vydání:	2024
Předmět:	Mathematics - Functional Analysis 44A12
Druh dokumentu:	Working Paper
Popis:	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. Comment: 41 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.20198 Zobrazit plný text záznamu View this record from Arxiv