Existence of Resonances in Metric Scattering
نویسنده
چکیده
We show that the resonances of a smooth super-exponentially decaying self-adjoint perturbation of the Laplacian in R n ; n 3 odd, determine the Minakshisundaram coeecients d j ; j 2; of the expansion of the regularized heat (wave) trace, provided that there are no negative eigenvalues and zero is not a resonance. We use this to prove the existence of innnitely many resonances for the perturbation of the Laplacian in R n , for n = 3; 5; by arbitrary smooth super-exponentially decaying metrics. If the metric perturbation is conformal to the Euclidean metric we show that there exist innnitely many resonances for any n 3 odd.
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