The Krein differential system and integral operators of random matrix theory

. Earlier, the Krein differential system has been studied under certain regularity conditions. In this paper, some cases are treated where these conditions are not fulfilled. Examples related to random matrix theory are studied.

[1]  L. Sakhnovich.  On Krein’s Differential System and its Generalization , 2006 .

[2]  Israel Gohberg,et al.  Theory and Applications of Volterra Operators in Hilbert Space , 2004 .

[3]  L. Sakhnovich.  Integrable operators and canonical differential systems , 2004, math/0403490.

[4]  S. Denisov.  To the spectral theory of Krein systems , 2002 .

[5]  L. Sakhnovich.  On Reducing the Canonical System to Two Dual Differential Systems , 2001 .

[6]  Lev A. Sakhnovich,et al.  Spectral Theory of Canonical Differential Systems. Method of Operator Identities , 1999 .

[7]  Alexander Its,et al.  A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics , 1997 .

[8]  L. Sakhnovich.  On properties of the discrete and continuous spectrum for the radial dirac equation , 1996 .

[9]  L. Sakhnovich.  Integral Equations with Difference Kernels on Finite Intervals , 1995 .

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

[11]  Allan P. Fordy,et al.  Factorization of operators.II , 1981 .

[12]  L. Sakhnovich.  EQUATIONS WITH A DIFFERENCE KERNEL ON A FINITE INTERVAL , 1980 .

[13]  G. Szegő.  Polynomials orthogonal on the unit circle , 1939 .

[14]  P. Sabatier,et al.  Inverse Problems in Quantum Scattering Theory , 1977 .

[15]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[16]  R. Bellman.  Stability theory of differential equations , 1953 .