## 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)

### MSC:

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

### Citations:

Zbl 0145.10604; Zbl 0235.34045
Full Text:

### References:

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