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Rodion Zaytsev

Publications and source records attributed to Rodion Zaytsev.

3 recordsLinked to original sources
arXiv2024

PSWF-Radon approach to reconstruction from band-limited Hankel transform

We give new formulas for reconstructions from band-limited Hankel transform of integer or half-integer order. Our formulas rely on the PSWF-Radon approach to super-resolution in multidimensional Fourier analysis. This approach consists of combining the theory of classical one-dimensional prolate spheroidal wave functions with the Radon transform theory. We also use the relation between Fourier and Hankel transforms and Cormack-type inversion of the Radon transform. Finally, we investigate numerically the capabilities of our approach to super-resolution for band-limited Hankel inversion in relation to varying levels of noise.

math.CA↗
arXiv2024

Insolvability of $x^x = a$ in elementary functions

In a recent paper "Solvability of equations in elementary functions" [arXiv:1911.10409] the insolvability in elementary functions of equation $\tan(x) - x = a$ was proved. This work applies the same topological method to prove the insolvability of equation $x^x = a$.

math.GM↗