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.
@article{104347, author = {Miloslav Nekvinda}, title = {On stable polynomials}, journal = {Applications of Mathematics}, volume = {34}, year = {1989}, pages = {177-196}, zbl = {0703.12001}, mrnumber = {0996895}, language = {en}, url = {http://dml.mathdoc.fr/item/104347} }
Nekvinda, Miloslav. On stable polynomials. Applications of Mathematics, Tome 34 (1989) pp. 177-196. http://gdmltest.u-ga.fr/item/104347/
Sur le nombre des racines d'une équation algébrique comprises entre des limites données, Crelles J. 52, 39 (1856).
A treatise on the stability of a given state of motion, London 1877.
Über die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt, Math. Ann. 46, 273 (1895). | Article | MR 1510884 | Zbl 0962.01500
Über die algebraischen Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen, Z. angew. Math. Mech, 1, 307 (1921). (1921) | Article
On the zeros of some elementary transcendental functions, (Russian) Izv. Ak. Nauk SSSR, Ser. Mat. 6 (1942), 115-134. English Translation: Amer. Math. Soc. Transl. (2) 1 (1955), 95-110. (1942) | MR 0073686 | Zbl 0068.05803
Über die algebraischen Kriterien für die Stabilität von Regulungsystemen, Math. Ann. 137 (1959), 328-350. (1959) | Article | MR 0104684
Introduction to Matrix Analysis, Mc Graw-Нill Book Company, New York 1960. (1960) | MR 0122820 | Zbl 0124.01001
Theory of Matrices, (Russian) Izd. Nauka, Moskva 1966. (1966) | MR 0202725
Lectures on the Mathematical Theory of Stability, (Russian) Izd. Nauka, Moskva 1967. (1967) | MR 0226126
Theory of Functional Differential Equations, Springer-Verlag, New York 1977. (1977) | MR 0508721 | Zbl 0352.34001