Multicentric calculus and the Riesz projection

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Abstract

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.
Original languageEnglish
Pages (from-to)127-145
Number of pages19
JournalJournal of Numerical Analysis and Approximation Theory
Volume44
Issue number2
Publication statusPublished - 17 Mar 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • multicentric calculus
  • lemniscate
  • Riesz projections
  • spectral projections
  • sign function of an operator

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