Abstract
Spectral properties of two-dimensional canonical systems with locally integrable Hamiltonian are studied. We give a criterion of discreteness of the spectrum of the associated selfadjoint operator, and study asymptotic distribution of this spectrum in terms of symmetrically normed ideals of compact operators. Simultaneously, we answer a 1968 question of Louis de Branges on description of the Hamiltonians which are structure functions of some de Branges spaces.
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Reference
R. Romanov, H. Woracek, Canonical systems with discrete spectrum, J. Funct. Anal. 278(4), Art. 108318 (2020)
Acknowledgements
The work of Roman Romanov is supported by the grant 17-11-01064 of Russian Science Foundation.
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Romanov, R., Woracek, H. (2021). Canonical Systems in Classes of Compact Operators. In: Abakumov, E., Baranov, A., Borichev, A., Fedorovskiy, K., Ortega-Cerdà, J. (eds) Extended Abstracts Fall 2019. Trends in Mathematics(), vol 12. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-74417-5_26
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DOI: https://doi.org/10.1007/978-3-030-74417-5_26
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-74416-8
Online ISBN: 978-3-030-74417-5
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