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A new approach to inverse spectral theory, III. Short-range potentials

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References

  1. I. Gelfand, D. Raikov and G. Shilov,Commutative Normed Rings, Chelsea, New York, 1964.

    Google Scholar 

  2. F. Gesztesy and B. Simon,A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure, preprint.

  3. B. Ya. Levin,Fourier- and Laplace-type transformations by means of solutions of a second-order differential equation, Dokl. Akad. Nauk SSSR106 (1956), 187–190 (Russian).

    MATH  MathSciNet  Google Scholar 

  4. V. A. Marchenko,Reconstruction of the potential energy from the phases of the scattered waves, Dokl. Akad. Nauk SSSR104 (1955), 695–698 (Russian).

    MATH  MathSciNet  Google Scholar 

  5. V. A. Marchenko,Sturm—Liouville Operators and Applications, BirkhÄuser, Basel—Boston-Stuttgart, 1986.

    MATH  Google Scholar 

  6. A. G. Ramm,Recovery of the potential from I-function, C. R. Math. Rep. Acad. Sci. Canada9 (1987), 177–182.

    MATH  MathSciNet  Google Scholar 

  7. A. G. Ramm,Multidimensional Inverse Scattering Problems, Longman, New York, 1992.

    MATH  Google Scholar 

  8. A. G. Ramm,Property C for ODE and applications to inverse problems, Proceedings of the International Conference on Operator Theory, to appear.

  9. A. G. Ramm and B. A. Taylor,Example of a potential in one-dimensional scattering problem for which there are infinitely many purely imaginary resonances, Phys. Lett.A124 (1987), 313–319.

    MathSciNet  Google Scholar 

  10. B. Simon,A new approach to inverse spectral theory, I. Fundamental formalism, Ann. of Math., to appear.

  11. M. Zworski,Distribution of poles for scattering on the real line, J. Fund Anal.73 (1987) 277–296.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Alexander Ramm.

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This material is based upon work supported by the National Science Foundation under Grant No. DMS-9707661. The Government has certain rights in this material.

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Ramm, A., Simon, B. A new approach to inverse spectral theory, III. Short-range potentials. J. Anal. Math. 80, 319–334 (2000). https://doi.org/10.1007/BF02791540

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