Upper and lower bounds on norms of functions of matrices |
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| Authors: | Anne Greenbaum |
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| Affiliation: | University of Washington, Mathematics Department, Box 354350, Seattle, WA 98195, United States |
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| Abstract: | Given an n by n matrix A, we look for a set S in the complex plane and positive scalars m and M such that for all functions p bounded and analytic on S and throughout a neighborhood of each eigenvalue of A, the inequalities m·inf{‖f‖L∞(S):f(A)=p(A)}?‖p(A)‖?M·inf{‖f‖L∞(S):f(A)=p(A)} |
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| Keywords: | Pick-Nevanlinna interpolation Blaschke product Nonnormal matrix Field of values Polynomial numerical hull |
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