Integral Equations and Operator Theory

, 71:407

Denjoy–Carleman Differentiable Perturbation of Polynomials and Unbounded Operators


  • Andreas Kriegl
    • Fakultät für MathematikUniversität Wien
  • Peter W. Michor
    • Fakultät für MathematikUniversität Wien
    • Fakultät für MathematikUniversität Wien

DOI: 10.1007/s00020-011-1900-5

Cite this article as:
Kriegl, A., Michor, P.W. & Rainer, A. Integr. Equ. Oper. Theory (2011) 71: 407. doi:10.1007/s00020-011-1900-5


Let \({t\mapsto A(t)}\) for \({t\in T}\) be a CM-mapping with values unbounded operators with compact resolvents and common domain of definition which are self-adjoint or normal. Here CM stands for Cω (real analytic), a quasianalytic or non-quasianalytic Denjoy–Carleman class, C, or a Hölder continuity class C0,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 CM-dependence on t of the eigenvalues and eigenvectors of A(t).

Mathematics Subject Classification (2010)



Perturbation theorydifferentiable choice of eigenvalues and eigenvectorsDenjoy–Carleman ultradifferentiable functions

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