The multiplicative structure on continuous polynomial valuations

By Semyon Alesker. 2004

115 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1b6203987d5322f9a134e7c961c8024c3b8a7cbc

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Citations in the corpus

Fisher information and matrix-valued valuations (2011, result): “See [24, 27] for information on the classical theory of valuations on convex sets and [1–5,9,11,16,19–22,28– 31, 33, 34, 43–45] for some of the more recent results.”
Projection bodies in complex vector spaces (2011, background): “The classical case A = R has attracted a lot of attention, we refer to [1, 2, 3, 4, 7, 8, 13, 20, 29] for some new developments.”
Minkowski Areas and Valuations (2010, background): “of elementary mixed volumes, valuations have become a critical notion (see [27, 31, 47] and see [1, 2, 3, 4, 5, 6, 11, 15, 29, 30, 49, 51, 52, 53] for some of the more recent contributions).”
Kinematic formulas for tensor valuations (2014, background): “(4) By Alesker’s Poincaré duality [8], there are isomorphisms pdc, pdm : Val sm → (Val)∗ defined by 〈pdc φ, ψ〉 := (φ ∗ ψ)0, φ, ψ ∈ Val, 〈pdm φ, ψ〉 := (φ · ψ)n, φ, ψ ∈ Val .”
Valuations on Sobolev spaces (2012, background): “See [25, 30, 47, 48] for information on the classical theory of valuations on convex bodies and [1, 2, 3, 4, 5, 9, 16, 21, 20, 22, 23, 33, 34, 35, 38, 39, 51, 53, 54, 58] for some of the more recent results.”
Difference bodies in complex vector spaces (2012, background): “This theory has been extended to the more general framework of manifolds instead of a real vector space, see for instance [5, 11].”
Theory of Valuations on Manifolds: A Survey (2006, methodology): “The proof of this theorem, besides the construction of the product from [6], uses the full generality of the Irreducibility Theorem.”