On zeros of self-reciprocal polynomials

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.

28 pages; v2 29 pages, revision of Sec.8, typos corrected, refs. added

Cited by in corpus (1)

• Limit laws of the coefficients of polynomials with only unit roots