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This article is cited in 47 scientific papers (total in 47 papers)
Research Papers
The space of isometry covariant tensor valuations
D. Hug, R. Schneider, R. Schuster Mathematisches Institut, Albert-Ludwigs-Universität, Freiburg i. Br., Germany
Abstract:
It is known that the basic tensor valuations which, by a result of S. Alesker, span the vector space of tensor-valued, continuous, isometry covariant valuations on convex bodies, are not linearly independent. P. McMullen has discovered linear dependences between these basic valuations and has implicitly raised the question as to whether these are essentially the only ones. The present paper provides a positive answer to this question. The dimension of the vector space of continuous, isometry covariant tensor valuations, of a fixed rank and of a given degree of homogeneity, is explicitly determined. The approach is constructive and permits one to provide a specific basis.
Keywords:
Convex body, tensor valuation, isometry covariance.
Received: 01.08.2006
Citation:
D. Hug, R. Schneider, R. Schuster, “The space of isometry covariant tensor valuations”, Algebra i Analiz, 19:1 (2007), 194–224; St. Petersburg Math. J., 19:1 (2008), 137–158
Linking options:
https://www.mathnet.ru/eng/aa108 https://www.mathnet.ru/eng/aa/v19/i1/p194
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Abstract page: | 542 | Full-text PDF : | 123 | References: | 47 | First page: | 2 |
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