Interpretation of the Schur-Cohn test in terms of canonical systems
Masatoshi Suzuki
TL;DR
This paper connects the Schur-Cohn test for polynomials with canonical systems by solving direct and inverse problems, providing a new interpretation of matrices and determinants in terms of Hamiltonians.
Contribution
It offers a novel interpretation of the Schur-Cohn test using canonical systems, advancing understanding of polynomial stability criteria.
Findings
Interpretation of matrices and determinants in Schur-Cohn test as Hamiltonians
Solutions to direct and inverse problems for two-dimensional canonical systems
Extension of the Schur-Cohn test framework to exponential polynomials
Abstract
We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation of the matrices and their determinants in the classical Schur-Cohn test for polynomials in terms of Hamiltonians of canonical system.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical functions and polynomials · Quantum chaos and dynamical systems