English

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.

Keywords

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

R2 v1 2026-06-23T20:39:58.303Z