On zeros of self-reciprocal polynomials

Masatoshi Suzuki

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arXiv · 1211.2953

On zeros of self-reciprocal polynomials

Masatoshi Suzuki

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Abstract

We establish a necessary and sufficient condition for all zeros of a self-reciprocal polynomial to lie on the unit circle. Moreover, we relate the necessary and sufficient condition with a canonical system of linear differential equations (in the sense of de Branges). This relationship enable us to understand that the property of a self-reciprocal polynomial having only zeros on the unit circle is equivalent to the positive semidefiniteness of Hamiltonians of corresponding canonical systems.

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Masatoshi Suzuki. 2012-12-14. On zeros of self-reciprocal polynomials. https://arxiv.org/abs/1211.2953

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