Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type |
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Authors: | N Çolako?lu M Hasanov B Ünalm?? Uzun |
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Institution: | (1) Department of Mathematics, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey |
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Abstract: | The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness
of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones
are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the
pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a
connection between the energetic stability condition and a perturbation problem for the coefficients is given. |
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Keywords: | Primary 47A75 Secondary 49R50 34L15 |
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