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Abstract Triangular Representation of Completely
Inversion of the theorem on the abstract triangular repre
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absolutely continuous arbitrary assertion Banach space boundary value problem canonical equation chain ty Chapter coincides complete chain completely continuous operator conjugate converges defined dimensional dissipative operator dissipative Volterra operator Dokl easily seen eigenvalues entire functions exists finite finite-dimensional operator following result formula H-matrix hence Hermitian Hilbert space inequality inessential extension integral equation interval invariant subspace invertible kernel Lemma Let us denote linear hull linear operator M. G. Krein M. S. Brodskii matrix-function maximal chain maximal eigenchain monodromy matrix multiplicators nonnegative nuclear imaginary component obtain obviously operator A G operators with nuclear orthogonal orthoprojectors partition positive type projectors proof of Theorem properties real component relation S-real satisfying the condition selfadjoint boundary value selfadjoint operator sequence signature matrix simple solution spectrum Theorem Theorem 2.1 theorem is proved theory transformator unicellular operators uniform norm unitary matrix V. I. Macaev vector vector-functions