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Cited by 7 publications
(14 citation statements)
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“…Theorem Assume that and hold and that errorRT(λ)errorR̲T(λ),S(λ)S̲(λ),λR, thefunctionalscriptG̲(·,λ0)ispositivedefiniteforsomeλ0<0.If n2(λ) and n̲2(λ) denote, respectively, the number of finite eigenvalues of (E j ) and ()E̲normalj in (,λ], then n2(λ)n̲2(λ)<forallλR. Proof The proof is based on a transformation of the eigenvalue problems (E j ) and ()E̲normalj into auxiliary augmented eigenvalue problems in dimension 2 n with separated boundary conditions, to which Theorem 4.1 is applied. Such a transformation is presented in [, Section 6.3]. We shall not repeat these technical arguments and the details are therefore omitted. Remark Similarly as in Remark 4.4 we can show that n2(λ)n̲2(...…”
Section: Comparison Of Finite Eigenvaluesmentioning
confidence: 88%
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“…Theorem Assume that and hold and that errorRT(λ)errorR̲T(λ),S(λ)S̲(λ),λR, thefunctionalscriptG̲(·,λ0)ispositivedefiniteforsomeλ0<0.If n2(λ) and n̲2(λ) denote, respectively, the number of finite eigenvalues of (E j ) and ()E̲normalj in (,λ], then n2(λ)n̲2(λ)<forallλR. Proof The proof is based on a transformation of the eigenvalue problems (E j ) and ()E̲normalj into auxiliary augmented eigenvalue problems in dimension 2 n with separated boundary conditions, to which Theorem 4.1 is applied. Such a transformation is presented in [, Section 6.3]. We shall not repeat these technical arguments and the details are therefore omitted. Remark Similarly as in Remark 4.4 we can show that n2(λ)n̲2(...…”
Section: Comparison Of Finite Eigenvaluesmentioning
confidence: 88%
“…The conditions below are slightly complicated as a price for allowing the (nonlinear) dependence on λ in the matrices representing the boundary conditions. The form of these conditions comes from the “symplectic structure” of linear Hamiltonian systems, as discussed in [, Section 6.1]. Let Rb(λ)=Qb(λ)Db(λ) be a polar decomposition of Rb(λ), i.e., Qb(λ) is orthogonal and Db(λ)0.…”
Section: Oscillation and Spectral Properties Of Linear Hamiltonian Symentioning
confidence: 99%
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