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A Formula for Finding a Potential from Nodal Lines
Author(s):
Joyce
R.
McLaughlin;
Ole
H.
Hald
Journal:
Bull. Amer. Math. Soc.
32
(1995),
241-247.
MSC (1991):
Primary 35R30, 35P20, 73D50
MathSciNet review:
1302784
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Additional information
References:
- [1]
- L. Friedlander, On certain spectral properties of very weak nonselfadjoint perturbations of selfadjoint operators, Trans. Moscow Math. Soc. 1 (1982), 185-218.
- [2]
- _____, On the spectrum of the periodic problem for the Schrödinger operator, Comm. Partial Differential Equations 15 (1990), 1631-1647. MR 1079606
- [3]
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- [4]
- O. H. Hald and J. R. McLaughlin, Solutions of inverse nodal problems, Inverse Problems 5 (1989), 307-347. MR 999065
- [5]
- _____, Inverse problems using nodal position data---uniqueness results, algorithms and bounds, Special Program on Inverse Problems (Proc. Centre Math. Anal., Austral. Nat. Univ.), vol. 17, Austral. Nat. Univ., Canberra, 1988, pp. 32-59. MR 1000355
- [6]
- _____, Inverse nodal problems: Finding the potential from nodal lines, Mem. Amer. Math. Soc. (to appear). MR 1370425
- [7]
- T. Kato, Perturbation theory for linear operators, Springer, New York, 1984.
- [8]
- J. R. McLaughlin, Inverse spectral theory using nodal points as data---a uniqueness result, J. Differential Equations 73 (1988), 354-362. MR 943946
- [9]
- J. Moser, Lectures on Hamiltonian systems, Mem. Amer. Math. Soc., vol. 81, Amer. Math. Soc., Providence, RI, 1968. MR 230498
- [10]
- K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20, 168. MR 72182
- [11]
- K. Uhlenbeck, Eigenfunctions of Laplace operators, Bull. Amer. Math. Soc. 78 (1972), 1073-1076. MR 319226
- [12]
- _____, Generic properties of eigenfunctions, Amer. J. Math. 98 (1976), 1059-1078. MR 464332
- [13]
- A. Weinman-Romer, Stabile Eigenwerte des Laplace-Operators auf Speziellen Tori, Diplomarbeit, ETH, Zürich, 1989.
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Additional Information:
DOI:
10.1090/S0273-0979-1995-00584-7
PII:
S 0273-0979(1995)00584-7
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