Orlicz valuations

Jin Li Shanghai University Gangsong Leng Shanghai University

Convex and Discrete Geometry mathscidoc:1703.40033

Indiana Univ. Math. J.
In this paper, Orlicz valuations compatible with $SL(n)$ transforms are classified. Unlike their $L_p$ analogs, the identity \text{operator} and the reflection operator are the only $SL(n)$ \text{compatible} Orlicz valuations (up to dilations). It turns out that the Orlicz projection body operator, the Orlicz centroid body operator and the Orlicz difference body operator are not Orlicz valuations. The property that the Orlicz difference body operator is not an Orlicz valuation plays an important role in characterizing the identity operator and the reflection operator.
Orlicz addition, Orlicz valuations, SL(n) contravari- ance, SL(n) covariance, Cauchy functional equation
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  • accepted
  author={Jin Li, and Gangsong Leng},
  booktitle={Indiana Univ. Math. J.},
Jin Li, and Gangsong Leng. ORLICZ VALUATIONS. In Indiana Univ. Math. J.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170310021143530924649.
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