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2000 | 74 | 1 | 51-64
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Integrable system of the heat kernel associated with logarithmic potentials

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
74
Numer
1
Strony
51-64
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-09-01
Twórcy
  • Graduate School of Mathematics, Nagoya University, Furo-cho 1, Chikusa-ku, Nagoya, Japan
Bibliografia
  • [1] L. Accardi, Vito Volterra and the development of functional analysis, in: Convegno Internazionale in memoria di Vito Volterra, Accademia Naz. dei Lincei, 1992, 151-181.
  • [2] K. Aomoto, Analytic structure of Schläfli function, Nagoya Math. J. 68 (1977), 1-16.
  • [3] K. Aomoto, Configurations and invariant Gauss-Manin connections of integrals I, II, Tokyo J. Math. 5 (1982), 249-287; 6 (1983), 1-24; Errata 22 (1999), 511-512.
  • [4] K. Aomoto, Formal integrable system attached to the statistical model of two dimensional vortices, in: Proc. Taniguchi Sympos. on Stochastic Differential Equations, 1985, 23-29.
  • [5] K. Aomoto, On some properties of the Gauss-ensemble of random matrices (integrable system), Adv. Appl. Math. 38 (1987), 385-399.
  • [6] K. Aomoto, Hypergeometric functions, The past, today, and ... (From the complex analytic point of view), Sugaku Expositions 9 (1996), 99-116.
  • [7] T. Hida, Brownian Motion, Springer, 1980.
  • [8] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Chap. 5, North-Holland/Kodan-sha, 1981.
  • [9] K. Ito, Wiener integral and Feynman integral, in: Proc. 4th Berkeley Sympos., 1961, 227-238.
  • [10] M. Kac, Integration in Function Spaces and Some of Its Applications, Scuola Norm. Sup., Pisa, 1980.
  • [11] P. Lévy, Problèmes Concrets d'Analyse Fonctionnelle, Gauthier-Villars, Paris, 1951.
  • [12] M. L. Mehta, Random Matrices, 2nd ed., Academic Press, Boston, 1991.
  • [13] J. Milnor, The Schläfli differential equality, in: Collected Papers I: Geometry, Publish or Perish, Houston, TX, 1994, 281-295.
  • [14] P. Orlik and H. Terao, Arrangements of Hyperplanes, Springer, 1992.
  • [15] L. Schläfli, On the multiple integral ∫∫...∫ whose limits are $p_1 = a_1x + b_1y+ ... +h_1z ≥ 0$ and $x^2 + y^2 + ... + z^2 = 1$, Quart. J. Math. 3 (1860), 54-68, 97-108.
  • [16] S. Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, Ann. Probab. 15 (1987), 1-39.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-apmv74z1p51bwm
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