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Эта публикация цитируется в 47 научных статьях (всего в 47 статьях)
Статьи
The space of isometry covariant tensor valuations
D. Hug, R. Schneider, R. Schuster Mathematisches Institut, Albert-Ludwigs-Universität, Freiburg i. Br., Germany
Аннотация:
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.
Ключевые слова:
Convex body, tensor valuation, isometry covariance.
Поступила в редакцию: 01.08.2006
Образец цитирования:
D. Hug, R. Schneider, R. Schuster, “The space of isometry covariant tensor valuations”, Алгебра и анализ, 19:1 (2007), 194–224; St. Petersburg Math. J., 19:1 (2008), 137–158
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa108 https://www.mathnet.ru/rus/aa/v19/i1/p194
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