Abstract
Consider a functionL(λ) defined on an interval Δ of the real axis whose values are linear bounded selfadjoint operators in a Hilbert spaceH. A point λ0 ∈ Δ and a vectorϕ0 ∈H(ϕ0 ≠ 0) are called eigenvalue and eigenvector ofL(λ) ifL(λ) ifL(λ0)ϕ0 = 0. Supposing that the functionL′(λ) can be represented as an absolutely convergent Fourier integral, the interval Δ is sufficiently small and the derivative will be positive at some point, it has been proved that all the eigenvectors of the operator-functionL(λ) corresponding to the eigenvalues from the interval Δ form an unconditional basis in the subspace spanned by them.
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