Trace formulas for non-self-adjoint periodic Schrödinger operators and some applications

Journal of Mathematical Analysis and Applications

Volumn 299, Issue 1, 2004, Pages 19-39

  Shin, Kwang C ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

Dirichlet and Neumann eigenvalues; Non self adjoint Hill operators; Trace formulas

Indexed keywords

EID: 4644363718     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.06.024     Document Type: Article

References (22)

1. M. Abramowitz I.E. Stegun Handbook of Mathematical Functions 1972 Dover New York
2. L.V. Ahlfors Complex Analysis 1979 McGraw-Hill New York
3. B. Birnir Complex Hill's equation and the complex periodic Korteweg-de Vries Equations Comm. Pure Appl. Math. 39 1986 1-49
4. G. Borg Eine Umkehrung der Sturm-Liouvillschen Eigenwertaufgabe Acta Math. 78 1946 1-96
5. S. Clark F. Gesztesy H. Holden B.M. Levitan Borg-type theorems for matrix-valued Schrödinger and Dirac operators J. Differential Equations 167 2000 181-210
6. 2ix
7. M.S.P. Eastham The Spectral Theory of Periodic Differential Equations 1973 Scottish Academic Press London
8. S. Flügge Practical Quantum Mechanics 1974 Springer New York
9. F. Gesztesy Integrable systems in the infinite genus limit Differential Integral Equations 14 2001 671-700
10. F. Gesztesy H. Holden Soliton Equations and Their Algebro-Geometric Solutions, vol. I: ( 1 -Dimensional Continuous Models Cambridge Stud. Adv. Math. vol. 79 2003 Cambridge Univ. Press
11. F. Gesztesy B. Simon The xi function Acta Math. 176 1996 49-71
12. F. Gesztesy R. Weikard Floquet theory revisited in: I. Knoeles (Ed.), Differential Equations and Mathematical Physics 1994 International Press Boston 67-84
13. M.G. Gasymov Spectral analysis of a class of second-order non-self-adjoint differential operators Funct. Anal. Appl. 14 1980 11-15
14. W. Magnus S. Winkler Hill's Equation 1979 Dover New York
15. H.P. McKean E. Trubowitz Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points Comm. Pure Appl. Math. 29 1976 143-226
16. V.A. Marchenko Sturm-Liouville Operators and Applications 1986 Birkhäuser Basel
17. L.A. Pastur V.A. Tkachenko Spectral theory of Schrödinger operators with periodic complex-valued potentials Funct. Anal. Appl. 22 1988 156-158
18. F.S. Rofe-Beketov The spectrum of non-selfadjoint differential operators with periodic coefficients Soviet Math. Dokl. 4 1963 1563-1566
19. K.C. Shin On half-line spectra for a class of non-self-adjoint Hill operators Math. Nachr. 261-262 2003 171-175
20. E.C. Titchmarsh Eigenfunction Expansions Associated with Second-Order Differential Equations, Part II 1958 Oxford Univ. Press New York
21. E. Trubowitz The inverse problem for periodic potentials Comm. Pure Appl. Math. 30 1977 321-337
22. Watson G.N. Theory of Bessel Functions Cambridge Univ. Press, New York 1996