On Wiegerinck`s support theorem


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.


Як цитувати

Logvinenko, V.; Logvinenko, D. On Wiegerinck`s Support Theorem. Мат. физ. анал. геом. 2002, 9, 352-368.





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