Abstract Classifications of SL ( n ) covariant function-valued valuations are established with some assumptions of continuity. New valuations, for example, weighted moment functions, are introduced and our classifications give unified characterizations of the Laplace transform on convex bodies, L p moment bodies, L p difference bodies, and polar L p moment bodies ( L − p intersection bodies). Using the new classifications, we also establish some Euler-type relations.

中文翻译：

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SL(n) 协变函数估值

摘要 SL ( n ) 协变函数估值的分类是在一些连续性假设下建立的。引入了新的估值，例如加权矩函数，并且我们的分类给出了凸体、L p 矩体、L p 差体和极性 L p 矩体（ L - p 相交体）上的拉普拉斯变换的统一表征。使用新的分类，我们还建立了一些欧拉类型的关系。