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Valuations on convex sets, non-commutative determinants, and pluripotential theory
Preprint
2004-01-19
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Abstract
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.