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An inverse spectral problem for a fractional Schrödinger operator

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Abstract

We establish that the potential appearing in a fractional Schrödinger operator is uniquely determined by an internal spectral data.

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References

  1. Bellassoued, M., Choulli, M., Dos-Santos-Ferreira, D., Kian, Y., Stefanov, P.: A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold. Ann. Inst. Fourier 17(6), 2471–2517 (2021)

    Article  MATH  Google Scholar 

  2. Bérard, P.H.: Spectral Geometry: Direct and Inverse Problems. With Appendixes by Gérard Besson, and by Bérard and Marcel Berger. Lecture Notes in Mathematics, 1207. Springer, Berlin (1986)

  3. Canuto, B., Kavian, O.: Determining coefficients in a class of heat equations via boundary measurements. SIAM J. Math. Anal. 32(5), 963–986 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fujiwara, D.: The asymptotic formula for the trace of Green operators of elliptic operators on compact manifold. Proc. Japan Acad. 43, 426–428 (1967)

    MathSciNet  MATH  Google Scholar 

  5. Ghosh, T., Lin, H.-Y., Xiao, J.: The Calderón problem for variable coefficients nonlocal elliptic operators. Comm. Partial Differential Equations 42(12), 1923–1961 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ghosh, T., Salo, M., Mikko, H., Uhlmann, G.: The Calderón problem for the fractional Schrödinger equation. Anal. PDE 13(2), 455–475 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  7. Helin, T., Lassas, M., Oksanen, L., Saksala, T.: Correlation based passive imaging with a white noise source. J. Math. Pures Appl. 116(9), 132–160 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  8. Nambu, T.: Characterization of the domain of fractional powers of a class of elliptic differential operators with feedback boundary conditions. J. Differential Equations 136(2), 294–324 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rüland, A., Salo, M.: The fractional Calderón problem: low regularity and stability. Nonlinear Anal. 193, 111529, 55 pp. (2020).

  10. Stinga, P.R., Zhang, C.: Harnack’s inequality for fractional nonlocal equations. Discrete Contin. Dyn. Syst. 33(7), 3153–3170 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yu, H.: Unique continuation for fractional orders of elliptic equations. Ann. PDE 3(2), Paper No. 16, 21 pp. (2017).

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Acknowledgements

I would like to thank the referee for his valuable comments.

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Correspondence to Mourad Choulli.

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The author is supported by the grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde).

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Choulli, M. An inverse spectral problem for a fractional Schrödinger operator. Arch. Math. 120, 395–402 (2023). https://doi.org/10.1007/s00013-023-01832-7

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  • DOI: https://doi.org/10.1007/s00013-023-01832-7

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