The Numerical Range of a Class of Self-adjoint Operator Functions

Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 179)


The structure of the numerical range and root zones of a class of operator functions, arising from one or two parameter polynomial operator pencils of waveguide type is studied. We construct a general model of such kind of operator pencils. In frame of this model theorems on distribution of roots and eigenvalues in some parts of root zones are proved. It is shown that, in general the numerical range and root zones are not connected but some connected parts of root zones are determined. It is proved that root zones, under some natural additional conditions which are satisfied for most of waveguide type multi-parameter spectral problems, are non-separated, i.e., they overlap.


Waveguide operator pencil numerical range root zone eigenvalue 

Mathematics Subject Classification (2000)

47A56 47A12 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of MathematicsIstanbul Technical UniversityMaslak, IstanbulTurkey

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