Proof of the BMV Conjecture

2011/07/25 by Stahl, Herbert R. · 2 citations
#15A15 #15A16 (Primary) 30F10 #44A10 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1107.4875

Abstract

We prove the BMV (Bessis, Moussa, Villani, 1975) conjecture, which states that the function t -> Tr exp(A-tB), t ≥ 0, is the Laplace transform of a positive measure on [0,∞) if A and B are n x n Hermitian matrices and B is positive semidefinite. A semi-explicit representation for this measure is given.

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