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 -