Abstract
In this paper the structure of infinite determinants corresponding to linear periodic ODE systems is investigated. Making use of the theory of Hilbert-Schmidt operators and their determinants it can be shown that the infinite determinant characterizing the stability of such an ODE system has polynomial structure. In the proof we use the fact that the trace of the commutator of two specific operators vanishes. The knowledge of the asymptotic structure of the finite section determinants enables us to improve the convergence of the infinite determinant which is the basis for numerical applications.
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Denk, R. (1998). On Hilbert-Schmidt operators and determinants corresponding to periodic ODE systems. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Differential and Integral Operators. Operator Theory: Advances and Applications, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8789-2_6
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DOI: https://doi.org/10.1007/978-3-0348-8789-2_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9774-7
Online ISBN: 978-3-0348-8789-2
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