Differentiability of functions of matrices
Functional Analysis
2007-05-23 v1 Representation Theory
Abstract
Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times differentiable so is the extension (likewise for analyticity and the class k+alpha).
Cite
@article{arxiv.math/0310086,
title = {Differentiability of functions of matrices},
author = {Yury Grabovsky and Omar Hijab and Igor Rivin},
journal= {arXiv preprint arXiv:math/0310086},
year = {2007}
}
Comments
12 pages