2013/01/14 by Montrieux, William Bordeaux
#FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1301.3102
We consider a non-self-adjoint pseudodifferential operator in the semi-classical limit (h→ 0). The principal symbol is given by p. We know that the resolvent (z-P)-1 exists inside the range up to a distance O((hln(1)/(h))(k)/(k+1)) from certain boundary points, where k∈\2,4,...\. In this work, we improve the resolvent estimates given by different authors in the case k=2 and in dimension one. For the proof, we will construct quasimodes by a scaling for z very close to the boundary. We give some applications of this formula.