Extension to other nonanalytic matrix functions

Establish whether the discrete Fourier transform and two-sided block-preconditioning techniques developed for oblique eigenprojection extend to other nonanalytic functions of a non-normal matrix.

Background

The paper's main construction applies a discrete Fourier transform to the matrix resolvent and uses two-sided block preconditioning to reduce the normalization factor for oblique eigenprojection. The authors note that the method is specifically enabled by a closed-form description of the Fourier modes of a single resolvent.

A broader unresolved question is whether analogous Fourier-transform and preconditioning structures exist for other nonanalytic matrix functions evaluated on non-normal inputs. A positive result could provide a general framework for quantum implementation of nonanalytic matrix functions beyond spectral-region indicators.