Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian
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 \textit{J. Sjöstrand} and \textit{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.
scientific article; zbMATH DE number 908028