arXiv math/04012192004-01math.MGmath.CV

Valuations on convex sets, non-commutative determinants, and pluripotential theory

Semyon Alesker

备注：: 39 pages. The definition of the quaternionic Hessian is replaced with the transposed matrix as it should be
发表信息：: Adv. Math. 195 (2005), no. 2, 561--595

英文摘要：

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space $\HH^n$ is presented. In particular new examples of $Sp(n)Sp(1)$-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables.

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