Accumulation of complex eigenvalues of a class of analytic operator functions. (English) Zbl 06875967
Summary: For analytic operator functions, we prove accumulation of branches of complex eigenvalues to the essential spectrum. Moreover, we show minimality and completeness of the corresponding system of eigenvectors and associated vectors. These results are used to prove sufficient conditions for eigenvalue accumulation to the poles and to infinity of rational operator functions. Finally, an application of electromagnetic field theory is given.
MSC:
| 47A56 | Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) |
| 47J10 | Nonlinear spectral theory, nonlinear eigenvalue problems |
| 47A10 | Spectrum, resolvent |
| 47A12 | Numerical range, numerical radius |
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