Hansen, Frank Trace functions as Laplace transforms. (English) Zbl 1111.47022 J. Math. Phys. 47, No. 4, 043504, 11 p. (2006). Summary: We study trace functions of the form \(t\mapsto \mathrm{Tr}f(A+tB)\) where \(f\) is a real function defined on the positive half-line and \(A\) and \(B\) are matrices such that \(A\) is positive definite and \(B\) is positive semidefinite. If \(f\) is non-negative and operator monotone decreasing, then such a trace function can be written as the Laplace transform of a positive measure. The question is related to the Bessis–Moussa–Villani conjecture [D.Bessis, P.Moussa and M.Villani, J. Math.Phys.16, No.11, 2318–2325 (1975; Zbl 0976.82501)]. Cited in 15 Documents MSC: 47A63 Linear operator inequalities 15A15 Determinants, permanents, traces, other special matrix functions 43A35 Positive definite functions on groups, semigroups, etc. Keywords:trace function; Laplace transform; Bessis-Moussa-Villani conjecture Citations:Zbl 0976.82501 PDFBibTeX XMLCite \textit{F. Hansen}, J. Math. Phys. 47, No. 4, 043504, 11 p. (2006; Zbl 1111.47022) Full Text: DOI arXiv References: [1] Araki H., Ann. Sci. Ec. Normale Super. 6 pp 67– (1973) [2] DOI: 10.1063/1.522463 · Zbl 0976.82501 · doi:10.1063/1.522463 [3] DOI: 10.1007/978-3-642-65755-9 · doi:10.1007/978-3-642-65755-9 [4] DOI: 10.1155/S0161171202011468 · Zbl 1001.15003 · doi:10.1155/S0161171202011468 [5] DOI: 10.1017/CBO9780511897191 · doi:10.1017/CBO9780511897191 [6] DOI: 10.1016/0024-3795(92)90268-F · Zbl 0745.15013 · doi:10.1016/0024-3795(92)90268-F [7] DOI: 10.2977/prims/1195145324 · Zbl 0902.47013 · doi:10.2977/prims/1195145324 [8] DOI: 10.1016/S0024-3795(01)00392-5 · Zbl 1034.47005 · doi:10.1016/S0024-3795(01)00392-5 [9] Hansen F., J. Inequal. Pure Appl. Math. 5 pp 16– (2004) [10] DOI: 10.2977/prims/1195164797 · Zbl 0829.46043 · doi:10.2977/prims/1195164797 [11] DOI: 10.1515/crll.1878.84.70 · doi:10.1515/crll.1878.84.70 [12] DOI: 10.1137/S0895479801387073 · Zbl 1007.68139 · doi:10.1137/S0895479801387073 [13] DOI: 10.1023/B:JOSS.0000019811.15510.27 · Zbl 1157.81313 · doi:10.1023/B:JOSS.0000019811.15510.27 [14] Nielsen H. P., Nyt Tidsskr. Mat. B 8 pp 86– (1897) [15] DOI: 10.1007/978-3-642-50824-0 · doi:10.1007/978-3-642-50824-0 [16] DOI: 10.2977/prims/1195143229 · Zbl 0969.47010 · doi:10.2977/prims/1195143229 [17] Widom H., Lecture Notes in Mathematics 1573, in: Linear and Complex Analysis Problem Book 3, Part 1 pp 266– (1994) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.