Spectral estimates for degenerate critical levels

Details Spectral estimates for degenerate critical levels Spectral estimates for degenerate critical levels

2005-03-30

arxiv.org/abs/math/0503719v2

Journal of Fourier Analysis and Applications, Volume 12, Number 5 / October 2006, 495-515

Mathematics

Analysis of PDEs

24 pages

Scientific paper

10.1007/s00041-005-5071-0

We establish spectral estimates at a critical energy level for $h$-pseudors . Via a trace formula, we compute the contribution of isolated (non-extremum) critical points under a condition of "real principal type". The main result holds for all dimensions, for a singularity of any finite order and can be invariantly expressed in term of the geometry of the singularity. When the singularities are not integrable on the energy surface the results are significative since the order w.r.t. $h$ of the spectral distributions are bigger than in the regular setting.

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