The Quadratic Numerical Range of an Analytic Operator Function |
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Authors: | Christiane Tretter |
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Institution: | 1.Institute of Mathematics,University of Bern,Bern,Switzerland |
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Abstract: | We introduce a new concept of numerical range for analytic operator functions. This so-called quadratic numerical range is
induced by a decomposition of the underlying Hilbert space. Like the classical numerical range of an operator function, it
is not convex, it has the spectral inclusion property, and it provides resolvent estimates and estimates for the lengths of
Jordan chains in boundary points having the exterior cone property. As the quadratic numerical range is contained in the numerical
range, it yields tighter enclosures for the eigenvalues and the spectrum of analytic operator functions. |
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Keywords: | |
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