2019
Том 71
№ 5

All Issues

Ochakovskaya O. A.

Articles: 3
Article (Russian)

Injectivity Classes of the Pompeiu Transformation

Ochakovskaya O. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1676-1684

New conditions for the injectivity of the Pompeiu transform for integral ball means are obtained. The main results substantially improve some known uniqueness theorems for functions with vanishing integrals over balls of fixed radius.

Article (Russian)

On the injectivity of the Pompeiu transform for integral ball means

Ochakovskaya O. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 3. - pp. 361-368

An uniqueness theorem is proved for functions in $\mathbb{R}^n, n \geq 2$, with vanishing integrals over balls of fixed radius and a given majorant of growth. The problem of the unimprovability of this theorem is considered.

Brief Communications (Russian)

Majorants of functions with vanishing integrals over balls

Ochakovskaya O. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 6. - pp. 857–861

We prove the existence of nontrivial functions in Rn , n > 2, with vanishing integrals over balls of fixed radius and given majoranta of growth.