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Simple proofs of some discrete domain stability related properties of multidimensional polynomials
Author(s) -
Basu S.,
Fettweis A.
Publication year - 1987
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490150404
Subject(s) - mathematical proof , simple (philosophy) , mathematics , polynomial , multivariable calculus , polydisc , property (philosophy) , domain (mathematical analysis) , stability (learning theory) , unit (ring theory) , pure mathematics , mathematical analysis , computer science , philosophy , geometry , mathematics education , epistemology , control engineering , machine learning , engineering
Simple and rigorous proofs of results due to various authors on tests for the property that a multivariable polynomial be devoid of zeros in the closed unit polydisc are given. the proof technique rests largely on a correct and complete formulation of the fact that the zeros of a polynomial are continuous functions of its coefficients. It is shown that almost all other related results can be derived in this manner.