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- Title
On the nature of the de Branges Hamiltonian.
- Authors
Kats, I.
- 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.
- Subjects
HILBERT space; BANACH spaces; HYPERSPACE; KREIN spaces; INDEFINITE inner product spaces
- Publication
Ukrainian Mathematical Journal, 2007, Vol 59, Issue 5, p718
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-007-0047-7