Harmonic Analysis of Translation Invariant Valuations

被引：84

作者：

Alesker, Semyon ^{[1
]}

Bernig, Andreas ^{[2
]}

Schuster, Franz E. ^{[3
]}

机构：

[1] Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math Sci, IL-69978 Tel Aviv, Israel

[2] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany

[3] TU Wien, Inst Diskrete Math & Geometrie, A-1040 Vienna, Austria

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2011年 / 21卷 / 04期

基金：

奥地利科学基金会;

关键词：

Valuation; algebraic integral geometry; tensor valuation; isoperimetric inequality; AFFINE ISOPERIMETRIC-INEQUALITIES; DUAL MIXED VOLUMES; CONVEX-BODIES; INTERSECTION BODIES; INTEGRAL GEOMETRY; PROJECTION BODIES; MINKOWSKI VALUATIONS; SETS; MANIFOLDS; SPACES;

D O I：

10.1007/s00039-011-0125-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：751 / 773

页数：23

共 53 条

[1] Projection bodies in complex vector spaces [J].