Fredholm determinants

The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.

[1]  加藤 敏夫 A short introduction to perturbation theory for linear operators , 1982 .

[2]  H. Weyl The Classical Groups , 1939 .

[3]  C. Tracy,et al.  Introduction to Random Matrices , 1992, hep-th/9210073.

[4]  M. Evans Munroe,et al.  Introduction to Measure and Integration , 1953 .

[5]  P. Levy Le mouvement brownien , 1955 .

[6]  F. Dyson Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[7]  Jim Hefferon,et al.  Linear Algebra , 2012 .

[8]  Freeman J. Dyson,et al.  Fredholm determinants and inverse scattering problems , 1976 .

[9]  E. Wigner On the Distribution of the Roots of Certain Symmetric Matrices , 1958 .

[10]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

[11]  J. Brian Conrey,et al.  The Riemann Hypothesis, Volume 50, Number 3 , 2003 .

[12]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[13]  W. T. Martin,et al.  The Wiener Measure of Hilbert Neighborhoods in the Space of Real Continuous Functions , 1944 .

[14]  M. Jimbo,et al.  Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent , 1980 .

[15]  C. Pöppe The fredholm determinant method for the KdV equations , 1984 .

[16]  Ivar Fredholm Sur une classe d’équations fonctionnelles , 1903 .

[17]  A. Einstein Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)] , 2005, Annalen der Physik.