Riccati map on L02(T) and its applications

Journal of Mathematical Analysis and Applications

Volumn 309, Issue 2, 2005, Pages 544-566

  Kappeler, Thomas ^a   Topalov, Peter ^a  

^a UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Hill operator; Riccati transform

Indexed keywords

EID: 22944455233     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.09.061     Document Type: Article

References (33)

1. A. Ambrosetti G. Prodi On the inversion of some differentiable maps between Banach spaces Ann. of Math. 93 1972 231-246
2. J. Bourgain Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, part II: KdV-equation Geom. Funct. Anal. 3 1993 209-262
3. H. Bueno C. Tomei Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type Nonlinearity 15 2002 1073-1077
4. C. Coleman J. McLaughlin Solution of the inverse spectral problem for an impedance with integrable derivative I Comm. Pure Appl. Math. 46 1993 145-184
5. C. Coleman J. McLaughlin Solution of the inverse spectral problem for an impedance with integrable derivative II Comm. Pure Appl. Math. 46 1993 185-212
6. J. Colliander M. Keel G. Staffilani H. Takaoka T. Tao Sharp global well-posedness for KdV and modified KdV on ℝ and T arXiv: Math.AP/ 0110045 v2
7. T. Kappeler C. Möhr Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator with singular potentials J. Funct. Anal. 186 2001 62-91
8. T. Kappeler, C. Möhr, P. Topalov, Birkhoff coordinates for KdV on phase spaces of distributions, Preprint Series, Institute of Mathematics, University of Zürich, 2003
9. T. Kappeler J. Pöschel KdV & KAM 2003 Springer-Verlag Berlin
10. -1 (T) and its applications, Preprint Series, Institute of Mathematics, University of Zürich, 2002
11. -1(T) and its applications Pliska Stud. Math. 15 2003
12. -1 (T, ℝ), Preprint Series, Institute of Mathematics, University of Zürich, 2003
13. 2(T) Internat. Math. Res. Notices 39 2004 2039-2068
14. C. Kenig P. Ponce L. Vega A bilinear estimate with applications to the KdV equations J. Amer. Math. Soc. 9 1996 573-603
15. E. Korotyaev Periodic weighted operators J. Differential Equations 189 2003 461-486
16. E. Korotyaev Inverse problems for periodic "weighted" operators J. Funct. Anal. 170 2000 188-218
17. E. Korotyaev Invariance principle for inverse problems Internat. Math. Res. Notices 38 2002 2007-2020
18. E. Korotyaev Characterization of spectrum for Schrödinger operator with periodic distributions Internat. Math. Res. Notices 37 2003 2019-2031
19. M. Krein The Basic Propositions of the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equation with Periodic Coefficients in memory of A.A. Andronov 1955 Izdat. Acad. Nauk SSSR Moscow pp. 413-498
20. M. Krein On the characteristic function A(λ) of a linear canonical system of differential equations of second order with periodic coefficients Prikl. Mat. Mekh. 21 1957 320-329
21. B. Levitan Inverse Sturm-Liouville Problems 1987 VNU Science Press Utrecht
22. M. Lyapunov Sur une équation transcendante et les équations differentielles linéaires du second ordre à coefficients périodiques C. R. Acad. Sci. Paris CXXXVIII 18 1899 1085-1088
23. J.-L. Lions E. Magenes Non-homogeneous Boundary Value Problems and Applications I Grundlehren Math. Wiss. vol. 181 1972 Springer-Verlag New York
24. W. Magnus S. Winkler Hill's Equation 1966 Interscience New York
25. V. Marchenko Sturm-Liouville Operators and Applications 1986 Birkhäuser Basel
26. H. McKean J. Scovel Geometry of some simple non-linear differential operators Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 1986 299-346
27. R. Miura Korteweg-de Vries equation and generalizations, I: A remarkable explicit nonlinear transformation J. Math. Phys. 9 1968 1202-1204
28. R. Miura The Korteweg-de Vries equation: A survey of results SIAM Rev. 18 1976 412-459
29. C. Möhr, thesis at the University of Zürich, 2001
30. M. Neuman-Zade A. Shkalikov Schrödinger operators with singular potentials from the space of multiplicators Math. Notes 66 1999 599-607
31. J. Pöschel E. Trubowitz Inverse Spectral Theory 1987 Academic Press San Diego
32. A. Savchuk A. Shkalikov Sturm-Liouville operators with singular potentials Math. Notes 66 1999 741-753
33. A. Savchuk On the eigenvalues and eigenfunctions of the Sturm-Liouville operator with singular potential Math. Notes 69 2001 245-252