The space of isometry covariant tensor valuations
作者： D. Hug , R. Schneider , R. Schuster
DOI: 10.1090/S1061-0022-07-00990-9
关键词: Isometry (Riemannian geometry) 、 Mathematics 、 Symmetric tensor 、 Tensor product of Hilbert spaces 、 Tensor density 、 Tensor 、 Mathematical analysis 、 Tensor product 、 Pure mathematics 、 Tensor contraction 、 Tensor field
摘要: It is known that the basic tensor valuations which, by a result of S. Alesker, span vector space valued, continuous, isometry covariant on convex bodies, are not linearly independent. P. McMullen has discovered linear dependences between these and implicitly raised question as to whether essentially only ones. The present paper provides positive answer this question. dimension valuations, fixed rank given degree homogeneity, explicitly determined. Our approach constructive permits one provide specific basis.
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