Denjoy–Carleman Differentiable Perturbation of Polynomials and Unbounded Operators


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)

26C10 26E10 47A55 


Perturbation theory differentiable choice of eigenvalues and eigenvectors Denjoy–Carleman ultradifferentiable functions 

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Andreas Kriegl
    • 1
  • Peter W. Michor
    • 1
  • Armin Rainer
    • 1
  1. 1.Fakultät für MathematikUniversität WienWienAustria

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