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Close Turning Points and the Harper Operator

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Fig. 2.

References

  1. M. Wilkinson, J. Phys. A 20 (13), 4337 (1987).

    Article  MathSciNet  Google Scholar 

  2. B. Helffer and J. Sjöstrand, Mem. Soc. Math. France (N. S.) 34, 1 (1988).

    Google Scholar 

  3. A. Avila and S. Jitomirskaya, Ann. of Math. (2) 170 (1), 303 (2009).

    Article  MathSciNet  Google Scholar 

  4. M. Wilkinson, Proc. Roy. Soc. London Ser. A 391 (1801), 305 (1984).

    Article  MathSciNet  Google Scholar 

  5. A. A. Fedotov, St. Petersburg Math. J. 25 (2), 303 (2013).

    Article  Google Scholar 

  6. J. P. Guillement, B. Helffer, and P. Treton, J. de Phys. 50, 2019 (1989).

    Article  Google Scholar 

  7. B. Helffer and J. Sjöstrand, Mem. Soc. Math. France (N. S.) 39, 1 (1989).

    Google Scholar 

  8. M. V. Fedoryuk, Asymptotic Analysis: Linear Ordinary Differential Equations (Springer-Verlag, Berlin–Heidelberg, 1993).

    Book  MATH  Google Scholar 

  9. A. Yu. Anikin, S. Yu. Dobrokhotov, and A. V. Tsvetkova, Theoret. and Math. Phys. 204 (2), 984 (2020).

    Article  MathSciNet  Google Scholar 

  10. A. A. Fedotov, Russ. J. Math. Phys. 29 (4), 467 (2022).

    Article  MathSciNet  Google Scholar 

  11. D. I. Borisov and A. A. Fedotov, Funct. Anal. Appl. 56 (4), 239 (2022).

    Article  MathSciNet  Google Scholar 

  12. V. Buslaev and A. Fedotov, Adv. Theor. Math. Phys. 5 (6), 1105 (2001).

    Article  MathSciNet  Google Scholar 

  13. V. S. Buslaev and A. A. Fedotov, St. Petersburg Math. J. 7 (4), 561 (1996).

    MathSciNet  Google Scholar 

  14. V. S. Buslaev and A. A. Fedotov, St. Petersburg Math. J. 6 (3), 495 (1994).

    Google Scholar 

  15. A. A. Fedotov and E. V. Shchetka, St. Petersburg Math. J. 29 (2), 363 (2018).

    Article  MathSciNet  Google Scholar 

  16. A. Fedotov and F. Klopp, Asymptot. Anal. 39 (3–4), 309 (2004).

    MathSciNet  Google Scholar 

  17. A. A. Fedotov and E. V. Shchetka, Math. Notes 104 (6), 933 (2018).

    Article  MathSciNet  Google Scholar 

  18. A. Fedotov and F. Klopp, Comm. Math. Phys. 227 (1), 1 (2002).

    Article  MathSciNet  Google Scholar 

  19. A. A. Fedotov and E. V. Shchetka, Math. Notes 107 (6), 1040 (2020).

    Article  MathSciNet  Google Scholar 

  20. A. Fedotov and E. Shchetka, Appl. Anal. 101 (1), 274 (2022).

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported by the Russian Foundation for Basic Research, grant no. 20-01-00451 A.

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Correspondence to A. A. Fedotov.

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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 785–790 https://doi.org/10.4213/mzm13932.

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Fedotov, A.A. Close Turning Points and the Harper Operator. Math Notes 113, 741–746 (2023). https://doi.org/10.1134/S0001434623050152

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