On the injectivity of the Pompeiu transform for integral ball means

• Date: 2011
• Main Authors: Ochakovskaya, O. A., Очаковская, О. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2722
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.