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 language | English |
|---|---|
| Pages (from-to) | 127-145 |
| Number of pages | 19 |
| Journal | Journal of Numerical Analysis and Approximation Theory |
| Volume | 44 |
| Issue number | 2 |
| Publication status | Published - 17 Mar 2016 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- multicentric calculus
- lemniscate
- Riesz projections
- spectral projections
- sign function of an operator