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Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques. (French) Zbl 0507.35066


MSC:

35P05 General topics in linear spectral theory for PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
65H10 Numerical computation of solutions to systems of equations
47A10 Spectrum, resolvent
35J10 Schrödinger operator, Schrödinger equation
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References:

[1] K Asada - D. Fujiwara , On some oscillatory integral transformation in L2(Rn) , Japan J. Math. , 4 ( 1978 ), pp. 299 - 361 . MR 528863 | Zbl 0402.44008 · Zbl 0402.44008
[2] R. Beals , A general calculus of pseudodifferential operators , Duke Math. J ,. 42 ( 1975 ), pp. 1 - 42 . Article | MR 367730 | Zbl 0343.35078 · Zbl 0343.35078
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[4] B. Helffer - D. Robert , Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques , Annales de l’Institut Fourier , 31 , fasc. 3 ( 1981 ), pp. 169 - 223 . Numdam | MR 638623 | Zbl 0451.35022 · Zbl 0451.35022
[5] B. Helffer - D. Robert , Comportement asymptotique précisé du spectre d’opérateurs globalement elliptiques dans Rn , C. R. Acad. Sci. Paris , 292 , 9 Février 1981 , p. 363 . MR 609080 | Zbl 0467.35074 · Zbl 0467.35074
[6] B. Helffer - D. Robert , Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques , C. R. Acad. Sci. Paris , 292 ( 1981 ), p. 47 . MR 610145 | Zbl 0465.35025 · Zbl 0465.35025
[7] L. Hörmander , The Weyl calculus of pseudodifferential operators , Comm. Pure Appl. Math. , 32 ( 1979 ), pp. 359 - 443 . MR 517939 | Zbl 0388.47032 · Zbl 0388.47032
[8] L. Hörmander , On the asymptotic distribution of eigenvalues of pseudo-differential operators in Rn , Ark. för Math ., 17 , no. 2 ( 1979 ), pp. 296 - 313 . MR 608322 · Zbl 0436.35064
[9] Pham The Lai - D. Robert , Valeurs propres d’une classe d’équations différentielles singulières sur une demi-droite , Ann. Scuola Norm. Sup. Pisa , Série IV , 6 , no. 2 ( 1979 ), pp. 335 - 366 . Numdam | MR 541452 | Zbl 0422.35062 · Zbl 0422.35062
[10] D. Robert , Propriétès spectrales d’opèrateurs pseudodifférentiels , Comm. Partial Diff. E quat. , 3 ( 1978 ), pp. 755 - 826 . MR 504628 | Zbl 0392.35056 · Zbl 0392.35056
[11] M.A. Subin , Pseudo-differential operators and spectral theory , Nauka , Moskva ( 1978 ). Zbl 0451.47064 · Zbl 0451.47064
[12] A. Voros , An algebra of pseudodifferential operators and the asymptotics of quantum mechanics , J. Functional Analysis , 29 , no. 1 ( 1978 ), pp. 104 - 132 . MR 496088 | Zbl 0386.47031 · Zbl 0386.47031
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