Local Spectral Deformation

摘要: ————————————————————————————————————— Abstract We develop an analytic perturbation theory for eigenvalues with finite multiplicities, embedded into the essential spectrum of a self-adjoint operator H. assume existence another A which family Hθ = e iθAHe−iθA extends analytically from real line to strip in complex plane. Assuming Mourre estimate holds i[H,A] vicinity eigenvalue, we prove that is locally deformed away leaving it isolated and thus permitting application Kato’s theory.