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arXiv · 1308.0228

An inverse problem for a class of canonical systems and its applications to self-reciprocal polynomials

Masatoshi Suzuki
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Abstract

A canonical system is a kind of first-order system of ordinary differential equations on an interval of the real line parametrized by complex numbers. It is known that any solution of a canonical system generates an entire function of the Hermite-Biehler class. In this paper, we deal with the inverse problem to recover a canonical system from a given entire function of the Hermite-Biehler class satisfying appropriate conditions. This type inverse problem was solved by de Branges in 1960s. However his results are often not enough to investigate a Hamiltonian of recovered canonical system. In this paper, we present an explicit way to recover a Hamiltonian from a given exponential polynomial belonging to the Hermite-Biehler class. After that, we apply it to study distributions of roots of self-reciprocal polynomials.

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Masatoshi Suzuki. 2013-08-01. An inverse problem for a class of canonical systems and its applications to self-reciprocal polynomials. https://arxiv.org/abs/1308.0228

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