Holomorphic factorization of polynomials

A. L. Pavlov

Donetsk National University, Donetsk, Ukraine

Abstract: We give necessary and sufficient conditions for a holomorphic factorization of an irreducible polynomial $P(s,\lambda)$, $s\in\mathbb C^n$, $\lambda\in\mathbb C$, in a domain $\Omega\subset\mathbb C^n$ which is connected with the ordering of the real part of the roots of the equation $P(s,\lambda)=0$, $s\in\Omega$.

Keywords: irreducible polynomial, factorization, holomorphic function.

UDC: 517.55

Received: 17.11.2014

DOI: 10.17377/smzh.2016.57.515

 English version: Siberian Mathematical Journal, 2016, 57:5, 860–865

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