Abstract
In this paper, a new Banach space ZH is defined, and it is proved that there is completeness of eigenfunction systems (symplectic orthogonal system) of a class of Hamiltonian system in ZH space. We have also proved the following results: ZH space can be continuously imbedded toL 2 [0, 1]×L 2 [0, 1], butZH ≠ L 2 [0,1] × L 1 [0, 1].
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Project supported by the National Natural Science Foundation of China
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Hongqing, Z., Alatancang The Hamiltonian system and completeness of symplectic orthogonal system. Appl Math Mech 18, 237–242 (1997). https://doi.org/10.1007/BF02453366
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DOI: https://doi.org/10.1007/BF02453366