Factorization of polynomials with analytic coefficients
arXiv:1202.6639
Abstract
We study monic univariate polynomials whose coefficients are analytic functions of a real variable and whose roots lie in a specified analytic curve. These include characteristic polynomials of unitary and hermitian matrices whose entries are analytic functions. We use a result of Newton to prove that every polynomial in such a class is a product of degree one polynomials in the class.
submitted for publication in Communications in Mathematics and Applications on 1 March 2012