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- W2117543441 abstract "Let S be a densely defined and closed symmetric relation in a Hilbert space ℋ︁ with defect numbers (1,1), and let A be some of its canonical selfadjoint extensions. According to Krein's formula, to S and A corresponds a so-called Q-function from the Nevanlinna class N. In this note we show to which subclasses Nγ of N the Q-functions corresponding to S and its canonical selfadjoint extensions belong and specify the Q-functions of the generalized Friedrichs and Krein-von Neumann extensions. A result of L. de Branges implies that to each function Q ∈ N there corresponds a unique Hamiltonian H such that Q is the Titchmarsh-Weyl coefficient of the two-dimensional canonical system Jy′ = —zHy on [0, ∞) where Weyl's limit point case prevails at ∞. Then the boundary condition y(0) = 0 corresponds to a symmetric relation Tmin with defect numbers (1,1) in the Hilbert space L2H, and Q is equal to the Q-function with respect to the extension corresponding to the boundary condition y1(0) = 0. If H satisfies some growth conditions at 0 or ∞, wepresent results on the corresponding Q-functions and show under which conditions the generalized Friedrichs or Krein-von Neumann extension exists." @default.
- W2117543441 created "2016-06-24" @default.
- W2117543441 creator A5045706261 @default.
- W2117543441 date "2002-03-01" @default.
- W2117543441 modified "2023-10-18" @default.
- W2117543441 title "On Generalized Friedrichs and Krein-von Neumann Extensions and Canonical Systems" @default.
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- W2117543441 doi "https://doi.org/10.1002/1522-2616(200203)236:1<175::aid-mana175>3.0.co;2-m" @default.
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