Weighted Weyl estimates near an elliptic trajectory
- Autores: Thierry Paul, Alejandro Uribe
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 14, Nº 1, 1998, págs. 145-165
- Idioma: inglés
- DOI: 10.4171/rmi/238
- Títulos paralelos:
- Estimaciones de Weyl ponderadas cerca de una trayectoria elíptica
- Enlaces
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Resumen
Let ?jh and Ejh denote the eigenfunctions and eigenvalues of a Schrödinger-type operator Hh with discrete spectrum. Let ?(x,?) be a coherent state centered at a point (x,?) belonging to an elliptic periodic orbit, ? of action S? and Maslov index s?. We consider weighted Weyl estimates of the following form: we study the asymptotics, as h ? 0 along any sequence h = S? / (2pl - a + s?), l Î N, a Î R fixed, of S|Ej - E| = ch |(?(x,?), ?jh)|2.
We prove that the asymptotics depend strongly on a-dependent arithmetical properties of c and on the angles ? of the Poincaré mapping of ?. 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.
