A ug 2 00 4 Valuations on convex sets , non - commutative determinants , and pluripotential theory
نویسنده
چکیده
A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn 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 developed by the author in two previous papers [5] and [6].
منابع مشابه
Valuations on convex sets , non - commutative determinants , and pluripotential theory
A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn 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 developed by the author in two previous papers [5] and [6].
متن کاملValuations, non-commutative determinants, and quaternionic pluripotential theory.
We present a new construction of translation invariant continuous valuations on convex compact subsets of a quaternionic space H n ≃ R4n. This construction is based on the theory of plurisubharmonic functions of quaternionic variables started by the author in [4] and [5] which is based in turn on the notion of non-commutative determinants. In this paper we also establish some new properties of ...
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The determinant is a main organizing tool in commutative linear algebra. In this review we present a theory of the quasideterminants defined for matrices over a division algebra. We believe that the notion of quasideterminants should be a main organizing tool in noncommutative algebra giving them the same role determinants play in commutative algebra.
متن کاملA ug 2 00 6 Theory of valuations on manifolds , IV . New properties of the multiplicative structure
This is the fourth part in the series of articles [4], [5], [6] (see also [3]) where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations is compatible with the product. Then it is proved that the Euler-Verdier involution on smooth valuations is an automorphism of the algebra of valuations. Then an integration functional on valuations wi...
متن کاملA ug 2 00 5 Theory of valuations on manifolds , II .
This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which satisfy some additional assumptions. The goal of this article is to introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish som...
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