Valuations on Log-Concave Functions

被引：1
|
作者：
Mussnig, Fabian [1 ]
机构：
[1] Tech Univ Wien, Inst Diskrete Math & Geometrie, Wiedner Hauptstr 8-10-1046, A-1040 Vienna, Austria
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 06期
基金：
奥地利科学基金会;
关键词：
Valuation; Log-concave function; SL(n) covariance; Translation covariance; Moment vector; Difference body; TRANSLATION INVARIANT VALUATIONS; P-MINKOWSKI VALUATIONS; CONVEX-SETS;
D O I：
10.1007/s12220-020-00539-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A classification of SL(n) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as SL(n) and translation invariant valuations on log-concave functions.
引用
收藏
页码：6427 / 6451
页数：25
相关论文
共 50 条
  • [21] THE STEINER SYMMETRIZATION OF LOG-CONCAVE FUNCTIONS AND ITS APPLICATIONS
    Lin, Youjiang
    Leng, Gangsong
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2013, 7 (04): : 669 - 677
  • [22] Grunbaum-type inequality for log-concave functions
    Meyer, Mathieu
    Nazarov, Fedor
    Ryabogin, Dmitry
    Yaskin, Vladyslav
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2018, 50 (04) : 745 - 752
  • [23] Log-concave and concave distributions in reliability
    Sengupta, D
    Nanda, AK
    NAVAL RESEARCH LOGISTICS, 1999, 46 (04) : 419 - 433
  • [24] Some Remarks on Petty Projection of Log-concave Functions
    da Silva, Leticia Alves
    Merino, Bernardo Gonzalez
    Villa, Rafael
    JOURNAL OF GEOMETRIC ANALYSIS, 2023, 33 (08)
  • [25] Rogers-Shephard inequality for log-concave functions
    Alonso-Gutierrez, David
    Merino, Bernardo Gonzalez
    Hugo Jimenez, C.
    Villa, Rafael
    JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (11) : 3269 - 3299
  • [26] Some Remarks on Petty Projection of Log-concave Functions
    Letícia Alves da Silva
    Bernardo González Merino
    Rafael Villa
    The Journal of Geometric Analysis, 2023, 33
  • [27] A Riesz representation theorem for functionals on log-concave functions
    Rotem, Liran
    JOURNAL OF FUNCTIONAL ANALYSIS, 2022, 282 (08)
  • [28] The Busemann-Petty problem on entropy of log-concave functions
    Niufa Fang
    Jiazu Zhou
    Science China(Mathematics), 2022, 65 (10) : 2171 - 2182
  • [29] LYZ ellipsoid and Petty projection body for log-concave functions
    Fang, Niufa
    Zhou, Jiazu
    ADVANCES IN MATHEMATICS, 2018, 340 : 914 - 959
  • [30] Log-concave sequences of bisnomial coefficients with their analogs and symmetric functions
    Bazeniar, Abdelghafour
    Ahmia, Moussa
    Bouchair, Abderrahmane
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2022, 53 (01): : 127 - 137
12345