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Hurwitz polynomials; expository paper; Hurwitz-Routh criterion; stable polynomial; Hermite; decompositon of Schur
The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
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