Approximation theory

Daghestan Electronic Mathematical Reports: Issue 12 (2019)


Inverse of the conic transformation of a function with a power weight

UDK: 517.5

Pages: 43 - 54


We consider the Radon transformation defined on circular cones called the conical Radon transform. In the three-dimensional space $R^{3}$, it maps the functions to its surface integrals over a circular cone, and in $R^{2}$ to its integrals over two rays with a common vertex. In this paper, we present new formulas for inversion of k-weighted conical and X-ray Radon transformations under complete and incomplete data in $R^{2}$ and $R^{3}$.


Keywords: conical transformation, k-weighted X-ray transformation, Radon transformation, inversion formula.




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