Spectral gaps of the periodic Schrödinger operator when its potential is an entire function

Advances in Applied Mathematics

Volumn 31, Issue 3, 2003, Pages 562-596

  Djakov, Plamen ^a   Mityagin, Boris ^b  

^a UNIVERSITY OF SOFIA   (Bulgaria)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142246421     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-8858(03)00027-7     Document Type: Article

References (15)

1. J. Avron, B. Simon, The asymptotics of the gap in the Mathieu equation, Ann. Physics 134 (1981) 76-84.
2. P. Djakov, B. Mityagin, Smoothness of Schroedinger operator potential in the case of Gevrey type asymptotics of the gaps, J. Funct. Anal. 195 (2002) 89-128.
3. P. Djakov, B. Mityagin, Spectral triangles of Schrödinger operators with complex potential, Preprint, 01-36, October 2001, 36 p.
4. B. Grébert, T. Kappeler, B. Mityagin, Gap estimates of the spectrum of the Zakharov-Shabat system, Appl. Math. Lett. 11 (1998) 95-97.
5. A. Grigis, Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill, Ann. Sci. Norm. Sup.20 (1987) 641-672.
6. E. Harrell, On the effect of the boundary conditions on the eigenvalues of ordinary differential equations, Amer. J. Math,, supplement 1981, dedicated to P. Hartman, John Hopkins Press, Baltimore.
7. H. Hochstadt, Estimates on the stability intervals for the Hill's equation, Proc. Amer. Math. Soc. 14 (1963) 930-932.
8. T. Kappeler, B. Mityagin, Gap estimates of the spectrum of Hill's equation and action variables for KdV, Trans. Amer. Math. Soc. 351 (1999) 619-646.
9. T. Kappeler, B. Mityagin, Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator, SIAM J. Math. Anal. 33 (2001) 113-152.
10. W. Magnus, S. Winkler, Hill's Equation, Interscience, 1969.
11. V.A. Marchenko, I.V. Ostrovskii, Characterization of the spectrum of Hill's operator, Mat. Sb. 97 (1975) 540-606; English transl.: Math. USSR-Sb. 26 (175).
12. T. Misyura, Properties of the spectra of periodic and antiperiodic boundary value problems generated Dirac operators I, Teor. Funktsii Funktsional. Anal. i Prilozhen. 30 (1978) 90-101, in Russian; II, Teor. Funktsii Funktsional. Anal. i Prilozhen. 31 (1979) 102-109.
13. J. Pöschel, E. Trubowitz, Inverse Spectral Theory, Academic Press, 1987.
14. V. Tkachenko, Non-selfadjoint periodic Dirac opeators, in: Oper. Theory Adv. Appl., Vol. 123, Birkhäuser, Basel, 2001, pp. 485-512.
15. V. Tkachenko, Characterization of Hill operators with analytic potentials, Integral Equations Operator Theory 41 (2001) 360-380.