Compactness of floquet isospectral sets for the matrix Hill's equation

Proceedings of the American Mathematical Society

Volumn 128, Issue 10, 2000, Pages 2933-2941

  Carlson, Robert ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

Hill's equation; Inverse spectral theory; KdV

Indexed keywords

EID: 23044524454     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-00-05634-3     Document Type: Article

References (13)

1. L. Ahlfors, Complex Analysis, McGraw-Hill, New York, 1966. MR 32:5844
2. B. Després, The Borg theorem for the vectorial Hill's equation, Inverse Problems 11 (1995), 97-121. MR 96a:34158
3. A. Finkel, E. Isaacson and E. Trubowitz, An explicit solution of the inverse periodic problem for Hill's equation, SIAM J. Math. Anal. 18 (1987), no. 1, 46-53. MR 88d:34037
4. C. Fulton and S. Pruess, Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems, Journal of Mathematical Analysis and Applications, 188 (1994), no. 1, 297-340. MR 96e:34144
5. J. Garnett and E. Trubowitz, Gaps and bands of one dimensional periodic Schrödinger operators, Comment. Math. Helvetici 59 (1984), 258-321. MR 85i:34004
6. K. Iwasaki, Inverse problem for Sturm-Liouville and Hill Equations, Annali di Matematica, Pura ed Applicata (1987), 185-206. MR 89d:34053
7. T. Kappeler, Fibration of the phase space for the Korteweg-De Vries equation, Annales de l'Institute Fourier 41 (1991), no. 1, 539-575. MR 92k:58212
8. P. Lax, Periodic solutions of the KdV equation, Communications on Pure and Applied Mathematics 28 (1975), 141-188. MR 51:6192
9. W. Magnus and S. Winkler, Hill's Equation, Dover, New York, 1979. MR 80k:34001
10. H.P. McKean and P. van Moerbeke, The spectrum of Hill's equation, Inventiones Math. 30 (1975), 217-274. MR 53:936
11. H.P. McKean and E. Trubowitz, Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points, Communications on Pure and Applied Mathematics 29 (1976), 143-226. MR 55:761
12. J. Ralston and E. Trubowitz, Isospectral sets for boundary value problems on the unit interval, Ergod. Th. and Dynam. Sys. 8 (1988), 301-358. MR 89m:34035
13. E. Trubowitz, The inverse problem for periodic potentials, Communications on Pure and Applied Mathematics 30 (1977), 321-337. MR 55:3408