Geometrical and Spectral Properties of Dilations
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چکیده
Proof. It would be easy to obtain these properties from the matrix form of U constructed in Sec. I.5.2, but we prefer to give a direct proof, independent of the particular realization of U . Part (i): To prove that L and L∗ are wandering subspaces, it suffices to show that UL0 ⊥L0 and UL0 ⊥ L0 for n = 1,2, . . .; by reason of symmetry it even suffices to consider one of these cases, say that of L0. Now for h,h′ ∈ H and n = 1,2, . . . we
منابع مشابه
Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
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Proof. It would be easy to obtain these properties from the matrix form of U constructed in Sec. I.5.2, but we prefer to give a direct proof, independent of the particular realization of U . Part (i): To prove that L and L∗ are wandering subspaces, it suffices to show that UL0 ⊥L0 and UL0 ⊥ L0 for n = 1,2, . . .; by reason of symmetry it even suffices to consider one of these cases, say that of...
متن کاملGeometrical and Spectral Properties of Dilations
Proof. It would be easy to obtain these properties from the matrix form of U constructed in Sec. I.5.2, but we prefer to give a direct proof, independent of the particular realization of U . Part (i): To prove that L and L∗ are wandering subspaces, it suffices to show that UL0 ⊥L0 and UL0 ⊥ L0 for n = 1,2, . . .; by reason of symmetry it even suffices to consider one of these cases, say that of...
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