Some remarks on CMV matrices and dressing orbits

International Mathematics Research Notices

Volumn , Issue 40, 2005, Pages 2437-2446

  Li, Luen Chau ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28444455973     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/imrn.2005.2437     Document Type: Review

References (16)

1. M. J. Ablowitz and J. F. Ladik, Nonlinear differential-difference equations and Fourier analysis, J. Math. Phys. 17 (1976), no. 6, 1011-1018.
2. M. Adler, On a trace functional for formal pseudo differential operators and the symplectic structure of the Korteweg-de Vries type equations, Invent. Math. 50 (1978/1979), no. 3, 219-248.
3. M. J. Cantero, L. Moral, and L. Velá zquez, Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle, Linear Algebra Appl. 362 (2003), 29-56.
4. P. Deift, L.-C. Li, and C. Tomei, Toda flows with infinitely many variables, J. Funct. Anal. 64 (1985), no. 3, 358-402.
5. V. Drinfel'd, Hamiltonian structures on Lie groups, Lie bialgebra, and the geometric meaning of the classical Yang-Baxter equations, Soviet Math. Dokl. 27 (1983), 68-71.
6. R. Killip and I. Nenciu, CMV: the unitary analogue of Jacobi matrices, preprint, 2005, http://arxiv.org/abs/math.SG/0508113.
7. B. Kostant, Quantization and representation theory, Representation Theory of Lie Groups, Proc. SRC/LMS Res. Symp., Oxford 1977 (M. Atiyah, ed.), LMS Lecture Notes Series, vol. 34, Cambridge University Press, Cambridge, 1979, pp. 287-316.
8. J.-H. Lu and A. Weinstein, Poisson Lie groups, dressing transformations, and Bruhat decompositions, J. Differential Geom. 31 (1990), no. 2, 501-526.
9. I. Nenciu, Lax pairs for the Ablowitz-Ladik system via orthogonal polynomials on the unit circle, Int. Math. Res. Not. 2005 (2005), no. 11, 647-686.
10. _, Lax pairs for the Ablowitz-Ladik system via orthogonal polynomials on the unit circle, Thesis, Caltech, May 2005.
11. T. Ratiu, On the smoothness of the time t-map of the KdV equation and the bifurcation of the eigenvalues of Hill's operator, Global Analysis (Proc. Biennial Sem. Canad. Math. Congr., Univ. Calgary, Calgary, Alta., 1978), Lecture Notes in Math., vol. 755, Springer, Berlin, 1979, pp. 248-294.
12. M. A. Semenov-Tian-Shansky, What is a classical r-matrix?, Funct. Anal. Appl. 17 (1983), 259-272.
13. _, Dressing transformations and Poisson group actions, Publ. Res. Inst. Math. Sci. 21 (1985), no. 6, 1237-1260.
14. B. Simon, Orthogonal Polynomials on the Unit Circle. Part 1, American Mathematical Society Colloquium Publications, vol. 54, American Mathematical Society, Rhode Island, 2005.
15. _, Orthogonal Polynomials on the Unit Circle. Part 2, American Mathematical Society Colloquium Publications, vol. 54, American Mathematical Society, Rhode Island, 2005.
16. G. Teschl, Jacobi Operators and Completely Integrable Nonlinear Lattices, Mathematical Surveys and Monographs, vol. 72, American Mathematical Society, Rhode Island, 2000.