# Integrable system of the heat kernel associated with logarithmic potentials

Annales Polonici Mathematici (2000)

- Volume: 74, Issue: 1, page 51-64
- ISSN: 0066-2216

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topAomoto, Kazuhiko. "Integrable system of the heat kernel associated with logarithmic potentials." Annales Polonici Mathematici 74.1 (2000): 51-64. <http://eudml.org/doc/208376>.

@article{Aomoto2000,

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.},

author = {Aomoto, Kazuhiko},

journal = {Annales Polonici Mathematici},

keywords = {Wiener integral; logarithmic potentials; Feynman-Kac formula; integrable system; heat kernel; logarithmic potential},

language = {eng},

number = {1},

pages = {51-64},

title = {Integrable system of the heat kernel associated with logarithmic potentials},

url = {http://eudml.org/doc/208376},

volume = {74},

year = {2000},

}

TY - JOUR

AU - Aomoto, Kazuhiko

TI - Integrable system of the heat kernel associated with logarithmic potentials

JO - Annales Polonici Mathematici

PY - 2000

VL - 74

IS - 1

SP - 51

EP - 64

AB - 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.

LA - eng

KW - Wiener integral; logarithmic potentials; Feynman-Kac formula; integrable system; heat kernel; logarithmic potential

UR - http://eudml.org/doc/208376

ER -

## References

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- [15] L. Schläfli, On the multiple integral ∫∫...∫ whose limits are ${p}_{1}={a}_{1}x+{b}_{1}y+...+{h}_{1}z\ge 0$ and ${x}^{2}+{y}^{2}+...+{z}^{2}=1$, Quart. J. Math. 3 (1860), 54-68, 97-108.
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