Entropy of a convolution operator

被引：5

作者：

Urbanski, A ^{[1
]}

机构：

[1] Natl Louis Univ, Nowy Sacz Sch Business, PL-33300 Nowy Sacz, Poland

来源：

OPEN SYSTEMS & INFORMATION DYNAMICS | 2004年 / 11卷 / 01期

关键词：

D O I：

10.1023/B:OPSY.0000024758.63038.dd

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The concept of the entropy of a doubly stochastic operator was introduced in 1999 by Ghys, Langevin, and Walczak. The idea was developed further by Kaminski and de Sam Lazaro, who also conjectured that the entropy of a convolution operator determined by a probability measure on a compact abelian group is equal to zero. We prove that this is true when the group is connected and the convolution operator is determined by a measure absolutely continuous with respect to the normalized Haar measure. Our result provides also a characterization of the set of doubly stochastic operators with non-zero entropy.

引用

页码：79 / 85

页数：7