# MathSciDoc: An Archive for Mathematician ∫

#### Rings and Algebrasmathscidoc:1701.31001

Acta Mathematica, 211, (2), 255-290, 2012.8
We prove the BMV (Bessis, Moussa, Villani, [1]) conjecture, which states that the function $${t \mapsto \mathop{\rm Tr}\exp(A-tB)}$$ , $${t \geqslant 0}$$ , is the Laplace transform of a positive measure on [0,∞) if$A$and$B$are $${n \times n}$$ Hermitian matrices and$B$is positive semidefinite. A semi-explicit representation for this measure is given.
BMV conjecture; Laplace transform; special matrix functions
@inproceedings{herbert2012proof,
title={Proof of the BMV conjecture},
author={Herbert R. Stahl},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401874251780},
booktitle={Acta Mathematica},
volume={211},
number={2},
pages={255-290},
year={2012},
}
Herbert R. Stahl. Proof of the BMV conjecture. 2012. Vol. 211. In Acta Mathematica. pp.255-290. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401874251780.