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Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

A note on analyticity and Floquet isospectrality

Author(s): Robert Carlson
Journal: Proc. Amer. Math. Soc. 134 (2006), 1447-1449.
MSC (2000): Primary 34B30
Posted: October 13, 2005
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Abstract | References | Similar articles | Additional information

Abstract: A simple argument shows that certain complex Hill's operators have the same Floquet multipliers as the zero potential case. Previous results are extended to include matrix coefficients and some meromorphic potentials.


References:

1.
E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, 1955. MR 0069338 (16:1022b)

2.
J. Duistermaat and F. Grünbaum, Differential equations in the spectral parameter, Comm. Math. Phys. 103 (1986), 177-240. MR 0826863 (88j:58106)

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 0871819 (88d:34037)

4.
M. Gasymov, Spectral analysis of a class of second-order non-self-adjoint differential operators, Functional Analysis and its Applications 14 (1980), 11-15. MR 0565091 (81c:47048)

5.
F. Gesztesy and R. Weikard, Picard potentials and Hill's equation on a torus, Acta Math. 176 (1996), 73-107. MR 1395670 (97f:14046)

6.
V. Goncharenko and A. Veselov, Monodromy of the matrix Schrödinger equations and Darboux transformations, J. of Phys. A, 31 (1998), 5315-5326. MR 1634885 (99g:34016)

7.
V. Guillemin and A. Uribe, Hardy functions and the inverse spectral method, Comm. in Partial Differential Equations, 8 (1983), 1455-1474. MR 0714048 (85h:35197)

8.
L. Pastur and V. Tkachenko, Spectral theory of Schrödinger operators with periodic complex-valued potentials, Functional Analysis and its Applications, 22 (1988), 156-158. MR 0947620 (89d:34056)

9.
K. Shin, On half-line spectra for a class of non-self-adjoint Hill operators, Math Nachr. 261/262 (2003), 171-175. MR 2020394 (2004i:34232)

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Additional Information:

Robert Carlson
Affiliation: Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, Colorado 80933
Email: carlson@math.uccs.edu

DOI: 10.1090/S0002-9939-05-08166-9
PII: S 0002-9939(05)08166-9
Received by editor(s): October 18, 2004
Received by editor(s) in revised form: December 16, 2004
Posted: October 13, 2005
Communicated by: Carmen C. Chicone
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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