Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure
By Semyon Alesker. 2005
49 citations recorded by the source corpus.
This is the fourth part in the series of articles math.MG/0503397, math.MG/0503399, math.MG/0509512 where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations introduced in math.MG/0503399 is compatible with the product. Then it is proved that the Euler-Verdier involution on smooth valuations introduced in math.MG/0503399 is an automorphism of the algebra of valuations. Then an integration functional on valuations with compact support is introduced, and a property of selfduality of valuations is proved. Next a space of generalized valuations is defined, and some basic properties of it are proved. Finally a canonical imbedding of the space of constructible functions on a real analytic manifold into the space of generalized valuations is constructed, and various structures on valuations are compared with known structures on constructible functions.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ed4113a692e4106b8149dd88a0b41a5c4ff20ecc
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In Applied Mathematics
- A. Bernig
- Joseph H. G. Fu
- Semyon Alesker
- G. Solanes
- Franz E. Schuster
- Thomas Wannerer
- Monika Ludwig
- Judit Abardia
In Geometry and Topology
- A. Bernig
- Joseph H. G. Fu
- Semyon Alesker
- G. Solanes
- Franz E. Schuster
- Monika Ludwig
- Thomas Wannerer
- Judit Abardia
In Mathematical Physics
- A. Bernig
- Joseph H. G. Fu
- G. Solanes
- Semyon Alesker
- Franz E. Schuster
- Thomas Wannerer
- Daniel Hug
- Christoph Haberl
Citations in the corpus
- Integral geometry of complex space forms (2012, background): “This follows from relation (3) from [6]; cf.”
- Theory of Valuations on Manifolds: A Survey (2006, background): “The second main point of Part IV [ A12 ] is introducing the notion of generalized valuations and establishing of basic properties of them.”
- Hermitian integral geometry (2008, background): “The following implies that δξμ extends by continuity to a smooth (but not translation-invariant) valuation in the sense of [5, 6, 7, 8, 9] (although we will not make use of this fact).”