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• W2060297998 abstract "Let V be a finite-dimensional real vector space. Let V al sm (V) be the space of translation-invariant smooth valuations on convex compact subsets of V. Let Dens(V) be the space of Lebesgue measures on V. The goal of the article is to construct and study an isomorphism $$ mathbb{F}_V :Val^{sm} (V)tilde to Val^{sm} (V^* ) otimes Dens(V) $$ such that $$ mathbb{F}_V $$ commutes with the natural action of the full linear group on both spaces, sends the product on the source (introduced in [5]) to the convolution on the target (introduced in [16]), and satisfies a Planchereltype formula. As an application, a version of the hard Lefschetz theorem for valuations is proved." @default.
• W2060297998 created "2016-06-24" @default.
• W2060297998 creator A5015373986 @default.
• W2060297998 date "2011-01-01" @default.
• W2060297998 modified "2023-09-27" @default.
• W2060297998 title "A fourier-type transform on translation-invariant valuations on convex sets" @default.
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• W2060297998 doi "https://doi.org/10.1007/s11856-011-0008-6" @default.
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