Integrable system of the heat kernel associated with logarithmic potentials

Kazuhiko Aomoto

Annales Polonici Mathematici (2000)

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

Abstract

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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.

How to cite

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Aomoto, 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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