Real Algebraic and Analytic Geometry
Submission: 2010, September 27.
This paper investigates hyperbolic polynomials with quasianalytic coefficients. Our main purpose is to prove factorization theorems for such polynomials, and next to generalize the results of K.~Kurdyka and L.~Paunescu about perturbation of analytic families of symmetric matrices to the quasianalytic settings.
Mathematics Subject Classification (2010): 14P15, 32B20, 15A18, 26E10.
Keywords and Phrases: quasianalytic perturbation, hyperbolic polynomials, quasianalytic and arc-quasianalytic functions, polynomially bounded structures, eigenvalues, eigenspaces, symmetric and antisymmetric matrices, spectral theorem, quasianalytic diagonalization.
Full text, 21p.: dvi 76k, pdf 294k.