Open Access
2013 Proof of the BMV conjecture
Herbert R. Stahl
Author Affiliations +
Acta Math. 211(2): 255-290 (2013). DOI: 10.1007/s11511-013-0104-z


We prove the BMV (Bessis, Moussa, Villani, [1]) conjecture, which states that the function tTrexp(A-tB) , t0 , is the Laplace transform of a positive measure on [0,∞) if A and B are n×n Hermitian matrices and B is positive semidefinite. A semi-explicit representation for this measure is given.

Funding Statement

Research supported by the grant STA 299/13-1 der Deutschen Forschungsgemeinschaft (DFG).


After this paper was accepted, the author sadly passed away in April 2013.


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Herbert R. Stahl. "Proof of the BMV conjecture." Acta Math. 211 (2) 255 - 290, 2013.


Received: 17 August 2012; Published: 2013
First available in Project Euclid: 31 January 2017

zbMATH: 1325.81089
MathSciNet: MR3143891
Digital Object Identifier: 10.1007/s11511-013-0104-z

Primary: 15A15
Secondary: 15A16 , 30F10 , 44A10

Keywords: BMV conjecture , Laplace transform , special matrix functions

Rights: 2013 © Institut Mittag-Leffler

Vol.211 • No. 2 • 2013
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