On Wiegerinck`s support theorem

Анотація

Let continuous function f(x), xÎℝⁿ, tend to 0 as ||x||®¥ faster than any negative degree of ||x||. Let Radon transform f ̅ (w, t), w Î ℝⁿ, ||w|| = 1, t Îℝ of f also tend to 0 as t®¥ and, besides, do it very fast on a massive enough set of w. In the paper, we describe the additional properties that f has under these assumptions for different rates of fast decreasing. In particular, the extremal case where f ̅ (w, t), has the compact support with respect to t for the open subset of unit sphere corresponds to Wiegerinck`s Theorem mentioned in the title.