On stable polynomials
Nekvinda, Miloslav
Applications of Mathematics, Tome 34 (1989), p. 177-196 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1989-01-01
Classification:  01A60,  12D10,  26C10,  30C15,  34D10,  93D99
@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/

Ch. Hermite Sur le nombre des racines d'une équation algébrique comprises entre des limites données, Crelles J. 52, 39 (1856).

J. Routh A treatise on the stability of a given state of motion, London 1877.

A. Hurwitz 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

J. Schur Über die algebraischen Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen, Z. angew. Math. Mech, 1, 307 (1921). (1921) | Article

L. S. Pontryagin 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

H. Cremer F. H. Effertz Über die algebraischen Kriterien für die Stabilität von Regulungsystemen, Math. Ann. 137 (1959), 328-350. (1959) | Article | MR 0104684

R. Bellman Introduction to Matrix Analysis, Mc Graw-Нill Book Company, New York 1960. (1960) | MR 0122820 | Zbl 0124.01001

F. R. Gantmacher Theory of Matrices, (Russian) Izd. Nauka, Moskva 1966. (1966) | MR 0202725

B. P. Demidowich Lectures on the Mathematical Theory of Stability, (Russian) Izd. Nauka, Moskva 1967. (1967) | MR 0226126

J. Hale Theory of Functional Differential Equations, Springer-Verlag, New York 1977. (1977) | MR 0508721 | Zbl 0352.34001