Proof of the BMV conjecture

Herbert R. Stahl

doi:10.1007/s11511-013-0104-z

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Home > Journals > Acta Math. > Volume 211 > Issue 2 > Article

2013 Proof of the BMV conjecture

Herbert R. Stahl

Author Affiliations +

Herbert R. Stahl¹
¹Beuth Hochschule/FB II, Luxemburger Str. 10, DE-13 353, Berlin, Germany

Acta Math. 211(2): 255-290 (2013). DOI: 10.1007/s11511-013-0104-z

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Abstract

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.