# Multicentric calculus and the Riesz projection

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**Multicentric calculus and the Riesz projection.** / Apetrei, Diana; Nevanlinna, Olavi.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Journal of Numerical Analysis and Approximation Theory*, vol. 44, no. 2 , pp. 127-145 .

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*Journal of Numerical Analysis and Approximation Theory*,

*44*(2 ), 127-145 .

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TY - JOUR

T1 - Multicentric calculus and the Riesz projection

AU - Apetrei, Diana

AU - Nevanlinna, Olavi

PY - 2016/3/17

Y1 - 2016/3/17

N2 - In multicentric holomorphic calculus one represents the function φ 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.

AB - In multicentric holomorphic calculus one represents the function φ 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.

KW - multicentric calculus

KW - lemniscate

KW - Riesz projections

KW - spectral projections

KW - sign function of an operator

M3 - Article

VL - 44

SP - 127

EP - 145

JO - Journal of Numerical Analysis and Approximation Theory

JF - Journal of Numerical Analysis and Approximation Theory

SN - 2457-6794

IS - 2

ER -

ID: 9309198