Enclosure of the numerical range of a class of non-selfadjoint rational operator functions. (English) Zbl 06805232
Summary: We introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range, the presented enclosure can be computed exactly in the infinite-dimensional case as well as in the finite-dimensional case. Moreover, the new enclosure is minimal given only the numerical ranges of the operator coefficients and many characteristics of the numerical range can be obtained by investigating the enclosure. We introduce a pseudonumerical range and study an enclosure of this set. This enclosure provides a computable upper bound of the norm of the resolvent.
MSC:
| 47A56 | Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) |
| 47B28 | Nonselfadjoint operators |
| 47A12 | Numerical range, numerical radius |
| 47J10 | Nonlinear spectral theory, nonlinear eigenvalue problems |
Keywords:
rational operator functions; nonlinear spectral problem; pseudonumerical range; numerical range; pseudospectra; resolvent estimateSoftware:
EigtoolReferences:
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