Open AccessExtremal properties of outer polynomial factors
Author(s) -
Scott McCullough
Publication year - 2003
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-03-07122-3
Subject(s) - algorithm , annotation , parenthesis , artificial intelligence , type (biology) , computer science , linguistics , biology , philosophy , ecology
If p ( s ) p(s) is a positive polynomial of degree 2 d 2d , then its outer factor q ( s ) q(s) has the property that the magnitude of each of its coefficients is larger than the magnitude of the corresponding coefficient of any other factor. In fact, this extremal property holds over vector-valued factorizations r ( s ) ∗ r ( s ) = p ( s ) r(s)^{*}r(s)=p(s) . Corollaries include a result for symmetric functions and complex conjugate pairs.