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Stahl’s Theorem (aka BMV Conjecture): Insights and Intuition on its Proof

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Spectral Theory and Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 254))

Abstract

The Bessis–Moussa–Villani conjecture states that the trace of exp(A — tB) is, as a function of the real variable t, the Laplace transform of a positive measure, where A and B are respectively a hermitian and positive semi-definite matrix. The long standing conjecture was recently proved by Stahl and streamlined by Eremenko. We report on a more concise yet self-contained version of the proof.

Mathematics Subject Classification (2010). 81V06, 82D06, 28B06, 30F06.

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Correspondence to Fabien Clivaz .

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Clivaz, F. (2016). Stahl’s Theorem (aka BMV Conjecture): Insights and Intuition on its Proof. In: Mantoiu, M., Raikov, G., Tiedra de Aldecoa, R. (eds) Spectral Theory and Mathematical Physics. Operator Theory: Advances and Applications, vol 254. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-29992-1_6

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