# zbMATH — the first resource for mathematics

Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian. (English) Zbl 0862.35082
The author obtains an asymptotic on the number of scattering poles (or resonances) of compactly supported hypoelliptic perturbations of $$-\Delta$$ in $$\mathbb{R}^n$$, $$n\geq 3$$, odd. By results of J. Sjöstrand and M. Zworski [Commun. Partial Differ. Equations 17, No. 5/6, 1021-1035 (1992; Zbl 0766.35031), J. Funct. Anal. 123, No. 2, 336-367 (1994; Zbl 0823.35137)] the problem is reduced to prove an asymptotic on the number of eigenvalues of the corresponding reference operator. Thus, many results of the author on upper bounds of the number of scattering poles for such perturbations are improved.

##### MSC:
 35P25 Scattering theory for PDEs 35P20 Asymptotic distributions of eigenvalues in context of PDEs 47F05 General theory of partial differential operators 47A40 Scattering theory of linear operators
Full Text: