Integral geometry of translation invariant functionals, II: The case of general convex bodies

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• 作者：Wolfgang Weil ^{wolfgang.weil@kit.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 52A20 ; 52A22 ; 60D05 ; secondary ; 52B45 ; 60G55
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：83
• 期：Complete
• 页码：145-171
• 全文大小：475 K

文摘

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.