2011/05/24 by Michael Hitrik, Hitrik, Michael, Karel Pravda‐Starov +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.AP #math.SP #msc:35H20 #msc:35P20 #msc:35S05 #msc:47A10 #msc:47B44
paper · pdf · doi:10.48550/arxiv.1105.4801
arxiv created 2011/05/24 · arxiv updated 2011/05/25
For a class of non-selfadjoint h--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of the spectrum of the operator in an \cal O(h)--neighborhood of the origin. Moreover, when all the singular spaces are reduced to zero, we establish accurate semiclassical resolvent estimates of subelliptic type, which depend directly on algebraic properties of the Hamilton maps associated to the quadratic approximations of the principal symbol.