Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599999 | Linear Algebra and its Applications | 2013 | 4 Pages |
Abstract
Let f(x)=âi=0naixi be a polynomial with positive coefficients and p>0. The pth Hadamard power of f(x) is the polynomial f[p](x)=âi=0naipxi. It is conjectured that if f(x) has only real zeros, then so does f[p](x) for p⩾1. We verify the conjecture when n=3 and give a counterexample when n=4. We also show that there exists a positive number Pn such that if f(x) has only real zeros, then so does f[p](x) for p>Pn.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yi Wang, Bin Zhang,