Multicentric calculus and the Riesz projection

Diana Apetrei; Olavi Nevanlinna

doi:10.33993/jnaat442-1064

Authors

Diana Apetrei Aalto University, Finland
Olavi Nevanlinna Aalto University, Finland

DOI:

https://doi.org/10.33993/jnaat442-1064

Keywords:

multicentric calculus, Riesz projection, spectral projections, sign function of an operator, lemniscates

Abstract views: 355

Abstract

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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References

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