论文信息 - The Knaster problem and the geometry of high-dimensional cubes

The Knaster problem and the geometry of high-dimensional cubes

Abstract We study questions of the following type: Given positive semi-definite matrix G , does there exist a sequence of vectors in R n whose Grammian equals to G and which has some specified additional properties (typically related to the sup norm )? In particular, we show that the answer to the 1947 Knaster problem about real functions on spheres is negative for sufficiently large dimensions. To cite this article: B.S. Kashin, S.J. Szarek, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Stanislaw J. Szarek | S. Szarek | B. Kashin | Boris Sergeevich Kashin

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