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Non-Selfadjoint Perturbations of Selfadjoint Operators in Two Dimensions IIIa. One Branching Point
Published online by Cambridge University Press: 20 November 2018
Abstract
This is the third in a series of works devoted to spectral asymptotics for non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, having a periodic classical flow. Assuming that the strength $\epsilon$ of the perturbation is in the range ${{h}^{2}}\ll \epsilon \ll {{h}^{1/2}}$ (and may sometimes reach even smaller values), we get an asymptotic description of the eigenvalues in rectangles $[-1/C,1/C]+i\epsilon [{{F}_{0}}-1/C,{{F}_{0}}+1/C],C\gg 1$, when $\epsilon {{F}_{0}}$ is a saddle point value of the flow average of the leading perturbation.
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- Copyright © Canadian Mathematical Society 2008
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