Factorization of Polynomials with Analytic Coefficients

Wayne Lawton

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.

Keywords


Analytic curve; Factorization; Germ; Newton's theorem

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DOI: http://dx.doi.org/10.26713%2Fcma.v4i1.157

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eISSN 0975-8607; pISSN 0976-5905