Título inglés | Weighted Weyl estimates near an elliptic trajectory. |
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Título español | Estimaciones de Weyl ponderadas cerca de una trayectoria elíptica. |
Autor/es | Paul, Thierry ; Uribe, Alejandro |
Organización | CEREMADE Univ. Paris IX-Dauphine, París, Francia;Math. Dep. Univ. Michigan, Ann Arbor (Michigan), Estados Unidos |
Revista | 0213-2230 |
Publicación | 1998, 14 (1): 145-165, 9 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | Let Ψjh and Ejh denote the eigenfunctions and eigenvalues of a Schrödinger-type operator Hh with discrete spectrum. Let Ψ(x,ξ) be a coherent state centered at a point (x,ξ) belonging to an elliptic periodic orbit, γ of action Sγ and Maslov index σγ. We consider weighted Weyl estimates of the following form: we study the asymptotics, as h → 0 along any sequence h = Sγ / (2πl - α + σγ), l Î N, α Î R fixed, of Σ|Ej - E| ≤ ch |(Ψ(x,ξ), Ψjh)|2. We prove that the asymptotics depend strongly on α-dependent arithmetical properties of c and on the angles θ of the Poincaré mapping of γ. In particular, under irrationality assumptions on the angles, the limit exists for a non-open set of full measure of c's. We also study the regularity of the limit as a function of c. |
Clasificación UNESCO | 120220 |
Palabras clave español | Ecuación de Schrödinger ; Autofunciones ; Autovalores ; Sistema hamiltoniano ; Trayectoria elíptica |
Código MathReviews | MR1639295 |
Código Z-Math | Zbl 0923.58055 |
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