학술논문
A continuity proof of Rudin's theorem for polynomials and a generalization
Document Type
Periodical
Author
Source
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications IEEE Trans. Circuits Syst. I Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on. 47(9):1319-1322 Sep, 2000
Subject
Language
ISSN
1057-7122
1558-1268
1558-1268
Abstract
We assign to each nonzero complex polynomial the minimum of the absolute values of its roots. We show the simple principle that this minimum depends continuously on the coefficients of the polynomial and is sufficiently powerful to give a very elementary proof of Rudin's stability theorem for multivariable polynomials. Moreover, we show that the polynomial version of a generalization on Rudin's theorem due to Hertz and Zeheb is obtained as a consequence of this principle.