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Structures on Valuations

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Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2177))

Abstract

In recent years on the space of translation invariant continuous valuations there have been discovered several canonical structures. Some of them turned out to be important for applications in integral geometry. In this chapter we review the relevant background and the main properties of the following new structures: product, convolution, Fourier type transform, and pull-back and push-forward of valuations under linear maps.

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Acknowledgements

Semyon Alesker is partially supported by ISF grant 1447/12.

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Authors and Affiliations

  1. Department of Mathematics, Tel Aviv University, Ramat Aviv, Israel

    Semyon Alesker

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  1. Semyon Alesker
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Correspondence to Semyon Alesker .

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Editors and Affiliations

  1. Department of Mathematics, Aarhus University, Aarhus C, Denmark

    Eva B. Vedel Jensen

  2. Department of Mathematics, Aarhus University, Aarhus C, Denmark

    Markus Kiderlen

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Alesker, S. (2017). Structures on Valuations. In: Jensen, E., Kiderlen, M. (eds) Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Lecture Notes in Mathematics, vol 2177. Springer, Cham. https://doi.org/10.1007/978-3-319-51951-7_3

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