Communications in Mathematical Physics

, Volume 146, Issue 1, pp 205-216

First online:

Sharp bounds on the number of scattering poles for perturbations of the Laplacian

  • Georgi VodevAffiliated withSection of Mathematical Physics, Institute of Mathematics, Bulgarian Academy of Sciences

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Sharp bounds on the numberN(r) of the scattering poles in the disc |z|≦r for a large class of compactly supported perturbations (not necessarily selfadjoint) of the Laplacian in ℝ n ,n≧3, odd, are obtained. In particular, in the elliptic case the estimateN(r)≦Cr n+C is proved.