Roots of Garding hyperbolic polynomials
Classical Analysis and ODEs
2021-04-21 v2
Abstract
We explore the regularity of the roots of Garding hyperbolic polynomials and real stable polynomials. As an application we obtain new regularity results of Sobolev type for the eigenvalues of Hermitian matrices and for the singular values of arbitrary matrices. These results are optimal among all Sobolev spaces.
Cite
@article{arxiv.2012.01077,
title = {Roots of Garding hyperbolic polynomials},
author = {Armin Rainer},
journal= {arXiv preprint arXiv:2012.01077},
year = {2021}
}
Comments
13 pages; some details added and typos corrected, accepted for publication in Proc. Amer. Math. Soc