Dot product invariant valuations on Lip$(S^{n-1})$

Andrea Colesanti; Daniele Pagnini; Ignacio Villanueva; Pedro Tradacete

Dot product invariant valuations on Lip$(S^{n-1})$

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arxiv 1906.04118 v2 pith:NJ2A5L42 submitted 2019-06-10 math.FA math.MG

Andrea Colesanti , Daniele Pagnini , Pedro Tradacete , Ignacio Villanueva This is my paper · ORCID

classification math.FAmath.MG

keywords invariantcontinuousproductvaluationsdefinedfunctionsintegrallipschitz

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abstract

We provide an integral representation for continuous, rotation invariant and dot product invariant valuations defined on the space Lip$(S^{n-1})$ of Lipschitz continuous functions on the unit $n-$sphere.

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A homogeneous decomposition theorem for valuations on convex functions
math.MG 2019-08 conditional novelty 7.0 of 10

Continuous, epi-translation invariant valuations on super-coercive convex functions decompose into homogeneous components of degrees 0 through n, and the degree-n valuations are exactly integrals of compactly supporte...

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