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| Completeness of the System of Root Vectors of 2 × 2 Upper Triangular Infinite-Dimensional Hamiltonian Operators in Symplectic Spaces and Applications |
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Citation： |
Hua WANG,ALATANCANG,Junjie HUANG.Completeness of the System of Root Vectors of 2 × 2 Upper Triangular Infinite-Dimensional Hamiltonian Operators in Symplectic Spaces and Applications[J].Chinese Annals of Mathematics B,2011,32(6):917~928 |
| Page view： 1768
Net amount： 1482 |
Authors： |
Hua WANG; ALATANCANG; Junjie HUANG; |
Foundation： |
by the National Natural Science Foundation of China (Nos. 10962004, 11061019), the
Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002),
the Chunhui Program of the Ministry of Education of China (No. Z2009-1-01010) and the Natural
Science Foundation of Inner Mongolia (Nos. 2009BS0101, 2010MS0110). |
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| Abstract： |
The authors investigate the completeness of the system of eigen or root vectors
of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H0. First, the
geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.
Next, some necessary and sufficient conditions for the completeness of the system of eigen
or root vectors of H0 are obtained. Finally, the obtained results are tested in several
examples. |
Keywords： |
2×2 upper triangular infinite-dimensional Hamiltonian operator,
Eigenvector, Root vector, Completeness |
Classification： |
47A70, 47A75, 47B99 |
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