Integrable system of the heat kernel associated with logarithmic potentials

Kazuhiko Aomoto

ArticleOriginal scientific text

Title

Integrable system of the heat kernel associated with logarithmic potentials

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Affiliations

Graduate School of Mathematics, Nagoya University, Furo-cho 1, Chikusa-ku, Nagoya, Japan

Abstract

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.

Keywords

ENG

Wiener integral, logarithmic potentials, Feynman-Kac formula, integrable system

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Title

Integrable system of the heat kernel associated with logarithmic potentials

Affiliations

Abstract

Keywords

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