Reciprocal polynomials with all zeros on the unit circle |
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Authors: | Do Yong Kwon |
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Affiliation: | 1.Department of Mathematics,Chonnam National University,Gwangju,Republic of Korea |
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Abstract: | Let f(x)=a d x d +a d−1 x d−1+⋅⋅⋅+a 0∈ℝ[x] be a reciprocal polynomial of degree d. We prove that if the coefficient vector (a d ,a d−1,…,a 0) or (a d−1,a d−2,…,a 1) is close enough, in the l 1-distance, to the constant vector (b,b,…,b)∈ℝ d+1 or ℝ d−1, then all of its zeros have moduli 1. |
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