Abstract
Let \({t\mapsto A(t)}\) for \({t\in T}\) be a C M-mapping with values unbounded operators with compact resolvents and common domain of definition which are self-adjoint or normal. Here C M stands for C ω (real analytic), a quasianalytic or non-quasianalytic Denjoy–Carleman class, C ∞, or a Hölder continuity class C 0,α. The parameter domain T is either \({\mathbb R}\) or \({\mathbb R^n}\) or an infinite dimensional convenient vector space. We prove and review results on C M-dependence on t of the eigenvalues and eigenvectors of A(t).
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AK was supported by FWF-Project P 23028-N13, PM by FWF-Project P 21030-N13, AR by FWF-Projects J 2771-N13 and P 22218-N13.
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Kriegl, A., Michor, P.W. & Rainer, A. Denjoy–Carleman Differentiable Perturbation of Polynomials and Unbounded Operators. Integr. Equ. Oper. Theory 71, 407 (2011). https://doi.org/10.1007/s00020-011-1900-5
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DOI: https://doi.org/10.1007/s00020-011-1900-5