Pruckner, R., & Woracek, H. (2022). A growth estimate for the monodromy matrix of a canonical system. Journal of Spectral Theory, 12(4), 1623–1657. https://doi.org/10.4171/JST/437
E101-01 - Forschungsbereich Analysis E058-02-3 - Fachgruppe Patent- und Lizenzmanagement E101 - Institut für Analysis und Scientific Computing E058-02 - Fachbereich Forschungs- und Transfersupport E058 - Forschungs-, Technologie- und Innovationssupport
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Journal:
Journal of Spectral Theory
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ISSN:
1664-039X
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Date (published):
2022
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Number of Pages:
35
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Publisher:
EUROPEAN MATHEMATICAL SOC
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Peer reviewed:
Yes
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Keywords:
Canonical system; asymptotic of eigenvalues; order of entire function
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Abstract:
We investigate the spectrum of 2-dimensional canonical systems in the limit circle case. It is discrete and, by the Krein–de Branges formula, cannot be more dense than the integers. But in many cases it will be more sparse. The spectrum of a particular selfadjoint realisation coincides with the zeroes of one entry of the monodromy matrix of the system. Classical function theory thus establishes an immediate connection between the growth of the monodromy matrix and the distribution of the spectrum.
We prove a general and flexible upper estimate for the monodromy matrix, use it to prove a bound for the case of a continuous Hamiltonian, and construct examples which show that this bound is sharp. The first two results run along the lines of earlier work by R. Romanov, but significantly improve upon these results. This is seen even on the rough scale of exponential order.
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Project title:
Order and type of canonical systems: P 30715-N35 (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Project (external):
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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Project ID:
Nonlinear Wave Equations and Krein-de Branges theory I4600
