Proof of the BMV conjecture

Herbert R. Stahl Beuth Hochschule/FB II, Luxemburger Str. 10, Berlin, Germany

Rings and Algebras mathscidoc: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
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  title={Proof of the BMV conjecture},
  author={Herbert R. Stahl},
  booktitle={Acta Mathematica},
Herbert R. Stahl. Proof of the BMV conjecture. 2012. Vol. 211. In Acta Mathematica. pp.255-290.
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