Integrable system of the heat kernel associated with logarithmic potentials
Volume 74 / 2000
Annales Polonici Mathematici 74 (2000), 51-64 DOI: 10.4064/ap-74-1-51-64
The heat kernel of a Sturm-Liouville operator with logarithmic potential can be described by using the Wiener integral associated with a real hyperplane arrangement. The heat kernel satisfies an infinite-dimensional analog of the Gauss-Manin connection (integrable system), generalizing a variational formula of Schläfli for the volume of a simplex in the space of constant curvature.