Abstract
We prove the theorem announced by the author in 1995 in the paper “A criterion for the discreteness of the spectrum of a singular canonical system” (Funkts. Anal. Prilozhen., 29, No. 3).
In developing the theory of Hilbert spaces of entire functions (we call them Krein-de Branges spaces), de Branges arrived at a certain class of canonical equations of phase dimension 2. He showed that, for any given Krein-de Branges space, there exists a canonical equation of the class indicated that restores a chain of Krein-de Branges spaces imbedded one into another. The Hamiltonians of such canonical equations are called de Branges Hamiltonians. The following question arises: Under what conditions will the Hamiltonian of a certain canonical equation be a de Branges Hamiltonian? The main theorem of the present work, together with Theorem 1 of the paper cited above, gives an answer to this question.
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References
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 5, pp. 658–678, May, 2007.
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Kats, I.S. On the nature of the de Branges Hamiltonian. Ukr Math J 59, 718–743 (2007). https://doi.org/10.1007/s11253-007-0047-7
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DOI: https://doi.org/10.1007/s11253-007-0047-7