real polynomial composition of Schur-Szegö real (positive/negative) root
Issue Date:
2014
Publisher:
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 40, No 2, (2014), 111p-128p
Abstract:
We consider real polynomials in one variable without root at 0 and without multiple roots. Given the numbers of the positive, negative and complex roots of two such polynomials, what can be these numbers for their composition of Schur-Szegö? We give the exhaustive answer to the question for degree 2, 3 and 4 polynomials and also in the case when the degree is arbitrary, the composed polynomials being with all roots real, and one of the polynomials having all roots but one of the same sign. 2010 Mathematics Subject Classification: 12D10.
