Proof of the BMV conjecture

DOI10.1007/s11511-013-0104-zzbMath1325.81089arXiv1107.4875OpenAlexW2066978207WikidataQ123220650 ScholiaQ123220650MaRDI QIDQ392793

Herbert R. Stahl

Publication date: 15 January 2014

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.4875

zbMATH Keywords

Laplace transformBessis-Moussa-Villani conjectureselfadjoint operator theory in quantum theoryspecial matrix functions

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace transform (44A10) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (20)

A positivity property of a quantum anharmonic oscillator suggested by the BMV conjecture ⋮ Sparse noncommutative polynomial optimization ⋮ Stahl’s Theorem (aka BMV Conjecture): Insights and Intuition on its Proof ⋮ On the roots of a hyperbolic polynomial pencil ⋮ Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials ⋮ More on operator monotone and operator convex functions of several variables ⋮ Proof of the BMV conjecture ⋮ Miscellaneous results related to the Gaussian product inequality conjecture for the joint distribution of traces of Wishart matrices ⋮ The Wigner distribution of n arbitrary observables ⋮ The Good Fortune of Maintaining a Long-Lasting Close Friendship and Scientific Collaboration with V. E. Katsnelson ⋮ On a special case of the Herbert Stahl theorem ⋮ The function \(\cosh {(\sqrt{a\,t^2+b})}\) is exponentially convex ⋮ On the BMV conjecture for \(2 \times 2\) matrices and the exponential convexity of the function \({\cosh (\sqrt{at^2+b})}\) ⋮ Real zero polynomials and A. Horn's problem ⋮ The matrix function \(e^{tA+B}\) is representable as the Laplace transform of a matrix measure ⋮ The tracial moment problem on quadratic varieties ⋮ Further implications of the Bessis-Moussa-Villani conjecture ⋮ The trace method for cotangent sums ⋮ Optimization over trace polynomials ⋮ On multivariate trace inequalities of Sutter, Berta, and Tomamichel

Cites Work

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• On the positivity of the coefficients of a certain polynomial defined by two positive definite matrices
• Principal minor sums of \((A + tB)^m\)
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• On an integral representation of the function Tr(exp(A-  B))
• ON THE REPRESENTATION OF Tr(e^(A-λB)) AS A LAPLACE TRANSFORM

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