Harmonic Analysis of Translation Invariant Valuations

Semyon Alesker; Andreas Bernig; Franz E. Schuster

doi:10.1007/s00039-011-0125-8

Harmonic Analysis of Translation Invariant Valuations

Semyon Alesker, Andreas Bernig^*, Franz E. Schuster

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

85 Scopus citations

Abstract

The decomposition of the space of continuous and translation-invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger-type theorem for continuous translation-invariant and SO(n)-equivariant tensor valuations is also given. As an application, symmetry properties of rigid-motion invariant and homogeneous bivaluations are established and then used to prove new inequalities of Brunn-Minkowski type for convex body valued valuations.

Original language	English
Pages (from-to)	751-773
Number of pages	23
Journal	Geometric and Functional Analysis
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s00039-011-0125-8
State	Published - Aug 2011

Keywords

Valuation
algebraic integral geometry
isoperimetric inequality
tensor valuation

Access to Document

10.1007/s00039-011-0125-8

Cite this

@article{8adad969feeb4b05850c6d5df0771b6f,

title = "Harmonic Analysis of Translation Invariant Valuations",

abstract = "The decomposition of the space of continuous and translation-invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger-type theorem for continuous translation-invariant and SO(n)-equivariant tensor valuations is also given. As an application, symmetry properties of rigid-motion invariant and homogeneous bivaluations are established and then used to prove new inequalities of Brunn-Minkowski type for convex body valued valuations.",

keywords = "Valuation, algebraic integral geometry, isoperimetric inequality, tensor valuation",

author = "Semyon Alesker and Andreas Bernig and Schuster, {Franz E.}",

year = "2011",

month = aug,

doi = "10.1007/s00039-011-0125-8",

language = "אנגלית",

volume = "21",

pages = "751--773",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Harmonic Analysis of Translation Invariant Valuations

AU - Alesker, Semyon

AU - Bernig, Andreas

AU - Schuster, Franz E.

PY - 2011/8

Y1 - 2011/8

N2 - The decomposition of the space of continuous and translation-invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger-type theorem for continuous translation-invariant and SO(n)-equivariant tensor valuations is also given. As an application, symmetry properties of rigid-motion invariant and homogeneous bivaluations are established and then used to prove new inequalities of Brunn-Minkowski type for convex body valued valuations.

AB - The decomposition of the space of continuous and translation-invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger-type theorem for continuous translation-invariant and SO(n)-equivariant tensor valuations is also given. As an application, symmetry properties of rigid-motion invariant and homogeneous bivaluations are established and then used to prove new inequalities of Brunn-Minkowski type for convex body valued valuations.

KW - Valuation

KW - algebraic integral geometry

KW - isoperimetric inequality

KW - tensor valuation

UR - http://www.scopus.com/inward/record.url?scp=80051679952&partnerID=8YFLogxK

U2 - 10.1007/s00039-011-0125-8

DO - 10.1007/s00039-011-0125-8

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:80051679952

SN - 1016-443X

VL - 21

SP - 751

EP - 773

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 4

ER -

Harmonic Analysis of Translation Invariant Valuations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this