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The Hamiltonian system and completeness of symplectic orthogonal system. (English) Zbl 0889.58041

Two new Banach spaces \(ZH_a\) and \(ZH_b\) are obtained. It is shown the completeness of the eigenfunction system (symplectic orthogonal system) of a class of Hamiltonian systems in the spaces \(ZH_a\) and \(ZH_b\). Also, it is proven that the \(ZH_b\) space can be continuously imbedded in \(V \times V\), where \(V\) is a Hilbert space. It is established that \(ZH_b \neq L_2[0,1] \times L_2 [0,1]\).
Reviewer: G.Zet (Iaşi)

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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References:

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