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Trace Formulae and Inverse Spectral Theory for Schr\"odinger Operators
Author(s):
F.
Gesztesy;
H.
Holden;
B.
Simon;
Z.
Zhao
Journal:
Bull. Amer. Math. Soc.
29
(1993),
250-255.
MSC (1991):
Primary 34A55, 34L40
MathSciNet review:
1215308
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References |
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Additional information
References:
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- J. Avron, P. H. M. van Mouche, and B. Simon, On the measure of the spectrum for the almost Mathieu operator, Comm. Math. Phys. \textbf{132} (1990), 103--118. MR 1069202
- [2]
- G. Borg, Uniqueness theorems in the spectral theory of $y''+(\lambda -q(x)) y=0$, Proc. 11th Scandinavian Congress of Mathematicians, Johan Grundt Tanums Forlag, Oslo, 1952, pp.~276--287. MR 58063
- [3]
- W. Craig, The trace formula for Schr\"odinger operators on the line, Comm. Math. Phys. \textbf{126} (1989), 379--407. MR 1027503
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- P. Deift and B. Simon, Almost periodic Schr\"odinger operators, \RM {III}. The absolutely continuous spectrum in one dimension, Comm. Math. Phys. \textbf{90} (1983), 389--411. MR 719297
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- F. Gesztesy, H. Holden, B. Simon, and Z. Zhao, Higher order trace relations for Schr\"odinger operators, Comm. Pure Appl. Math. MR
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- F. Gesztesy, H. Holden, and B. Simon, Absolute summability of the trace relation for certain Schr\"odinger operators, Comm. Math. Phys., to be submitted. MR
- [9]
- S. Kotani, Ljapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schr\"odinger operators, Stochastic Analysis (K. Ito, ed.), North-Holland, Amsterdam, 1984, pp.~225--247. MR 780760
- [10]
- S. Kotani and M. Krishna, Almost periodicity of some random potentials, J. Funct. Anal. \textbf{78} (1988), 390--405. MR 943504
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- M. G. Krein, Perturbation determinants and a formula for the traces of unitary and self-adjoint operators, Soviet Math. Dokl. \textbf{3} (1962), 707--710. MR
- [12]
- Y. Last, A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants, Comm. Math. Phys. \textbf{151} (1993), 183--192. MR 1201659
- [13]
- H. P. McKean and P. van Moerbeke, The spectrum of Hill\RM 's equation, Invent. Math. \textbf{30} (1975), 217--274. MR 397076
- [14]
- B. Simon, Kotani theory for one-dimensional stochastic Jacobi matrices, Comm. Math. Phys. \textbf{89} (1983), 227--234. MR 709464
- [15]
- E. Trubowitz, The inverse problem for periodic potentials, Comm. Pure Appl. Math. \textbf{30} (1977), 321--337. MR 430403
- [16]
- S. Venakides, The infinite period limit of the inverse formalism for periodic potentials, Comm. Pure Appl. Math. \textbf{41} (1988), 3--17. MR 917122
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00431-2
PII:
S 0273-0979(1993)00431-2
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