The multiplicative structure on polynomial continuous valuations

Abstract

We introduce a canonical structure of a commutative associative filtered algebra with the unit on polynomial smooth valuations, and study its properties. The induced structure on the subalgebra of translation invariant smooth valuations has especially nice properties (it is the structure of the Frobenius algebra). We also present some applications.

28 pages, misprints

References in corpus (1)

• Algebraic structures on valuations, their properties and applications

Cited by in corpus (9)

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• Structure of the unitary valuation algebra
• $\mathrm{SL}(m,C)$-equivariant and translation covariant continuous tensor valuations
• Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations
• Plurisubharmonic functions on the octonionic plane and Spin(9)-invariant valuations on convex sets
• A Fourier type transform on translation invariant valuations on convex sets