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- W2935232227 abstract "We study spectral properties of two-dimensional canonical systems $y'(t)=zJH(t)y(t)$, $tin[a,b)$, where the Hamiltonian $H$ is locally integrable on $[a,b)$, positive semidefinite, and Weyl's limit point case takes place at $b$. We answer the following questions explicitly in terms of $H$: Is the spectrum of the associated selfadjoint operator discrete ? If it is discrete, what is its asymptotic distribution ? Here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast. Making an analogy with complex analysis, this corresponds to convergence class and type w.r.t. proximate orders having order larger than $1$. It is a surprising fact that these properties depend only on the diagonal entries of $H$. In 1968 this http URL~Branges posed the following question as a fundamental problem: Which Hamiltonians are the structure Hamiltonian of some de~Branges space ? We give a complete and explicit answer." @default.
- W2935232227 created "2019-04-11" @default.
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- W2935232227 date "2019-04-07" @default.
- W2935232227 modified "2023-09-27" @default.
- W2935232227 title "Canonical systems with discrete spectrum" @default.
- W2935232227 hasPublicationYear "2019" @default.
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