Strong limit-point classification of singular Hamiltonian expressions. (English) Zbl 1054.34041

The authors investigate singular Hamiltonian differential systems with complex coefficients of the form \(Lz:=Jz'-Q(t)z=\lambda P(t)z\), where \(\lambda\) is a complex parameter, \[ J=\left(\begin{matrix} 0&-I\\ I&0 \end{matrix}\right),\quad Q(t)=\left( \begin{matrix} -C(t)&A^\ast(t)\\ A(t)&B(t) \end{matrix}\right),\quad P(t)=\left( \begin{matrix} W(t)& 0\\ 0&0 \end{matrix}\right), \] \(A,\;B,\;C,\;W\) are locally integrable \(n\times n\)-matrix-valued functions on \([0,\infty)\), \(B,C,W\) are Hermitian with \(W>0\). They give strong limit-point criteria for the operator \(L\) generated by the system, which extend the results due to Everitt, Giertz and Weidmann for the scalar case, see [W. N. Everitt, J. Lond. Math. Soc. 41, 531–534 (1966; Zbl 0145.10604) and W. N. Everitt, M. Giertz and J. Weidmann, Math. Ann. 200, 335–346 (1973; Zbl 0235.34045)].
Reviewer: Pavel Rehak (Brno)


34B20 Weyl theory and its generalizations for ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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