Multicentric calculus and the Riesz projection
In multicentric holomorphic calculus one represents the function ? using a new polynomial variable \(w = p(z)\) in such a way that when evaluated at the operator \(p(A)\) is small in norm. Here it is assumed that \(p\) has distinct roots. In this paper we discuss two related problems, separating a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2015-12-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1064 |
| Summary: | In multicentric holomorphic calculus one represents the function ? using a new polynomial variable \(w = p(z)\) in such a way that when evaluated at the operator \(p(A)\) is small in norm. Here it is assumed that \(p\) has distinct roots. In this paper we discuss two related problems, separating a compact set, such as the spectrum, into different components by a polynomial lemniscate, and then applying the calculus for computation and estimation of the Riesz spectral projection. It may then be desirable to move to using \(p(z)^n\) as a new variable and we develop the necessary modifications to incorporate the multiplicities in the roots.
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| ISSN: | 2457-6794 2501-059X |