Lower bounds for Schrödinger operators in H¹(ℝ)

Pouliquen, Ronan

Studia Mathematica, Tome 133 (1999), p. 79-89 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove trace inequalities of type $| | u^{'} {| |}_{L^{2}}^{2} + \sum_{j \in ℤ} k_{j} | u (a_{j}) |^{2} {\geq λ | | u | |}_{L^{2}}^{2}$ where $u \in H^{1} (ℝ)$ , under suitable hypotheses on the sequences ${a_{j}}_{j \in ℤ}$ and ${k_{j}}_{j \in ℤ}$ , with the first sequence increasing and the second bounded.

Publié le : 1999-01-01

Zbl 0923.35110

EUDML-ID : urn:eudml:doc:216587

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     author = {Ronan Pouliquen},
     title = {Lower bounds for Schr\"odinger operators in H$^1$($\mathbb{R}$)},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {79-89},
     zbl = {0923.35110},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv132i1p79bwm}
}

Pouliquen, Ronan. Lower bounds for Schrödinger operators in H¹(ℝ). Studia Mathematica, Tome 133 (1999) pp. 79-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv132i1p79bwm/

Bibliographie

[00000] [Al-Ge] S. Albeverio, F. Gesztesy, R. Hοegh-Krohn and H. Holden, Solvable Models in Quantum Mechanics, Springer, Berlin, 1988. | Zbl 0679.46057

[00001] [Fe-Ph] C. Fefferman and D. H. Phong, The uncertainty principle and sharp Gårding inequalities, Comm. Pure Appl. Math. 34 (1981), 285-331. | Zbl 0458.35099

[00002] [Ga-Ol] G. V. Galunov and V. L. Oleĭnik, Analysis of the dispersion equation for a negative Dirac "comb", St. Petersburg Math. J. 4 (1993), 707-720.

[00003] [Ke-Sa] R. Kerman and E. Sawyer, The trace inequality and eigenvalue estimates for Schrödinger operators, Ann. Inst. Fourier (Grenoble) 36 (1986), no. 4, 207-228. | Zbl 0591.47037

[00004] [Le-No] N. Lerner and J. Nourrigat, Lower bounds for pseudo-differential operators, ibid. 40 (1990), 657-682. | Zbl 0703.35182

[00005] [Pou] R. Pouliquen, Uncertainty principle and Schrödinger operators with potential localized on hypersurfaces, Preprint Univ. Bretagne Occidentale, Fasc. 5 (1997).

[00006] [Re-Si] M. Reed and B. Simon, Methods of Modern Mathematical Physics II. Fourier Analysis, Self-adjointness, Academic Press, 1972.

[00007] [Str] R. Strichartz, Uncertainty principles in harmonic analysis, J. Funct. Anal. 84 (1989), 97-114. | Zbl 0682.43005