On zeros of self-reciprocal polynomials
Classical Analysis and ODEs
2012-12-18 v2 Functional Analysis
Number Theory
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.
Cite
@article{arxiv.1211.2953,
title = {On zeros of self-reciprocal polynomials},
author = {Masatoshi Suzuki},
journal= {arXiv preprint arXiv:1211.2953},
year = {2012}
}
Comments
28 pages; v2 29 pages, revision of Sec.8, typos corrected, refs. added