Corpus ID: 119717903

On zeros of self-reciprocal polynomials

@article{Suzuki2012OnZO,
  title={On zeros of self-reciprocal polynomials},
  author={Masatoshi Suzuki},
  journal={arXiv: Classical Analysis and ODEs},
  year={2012}
}
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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