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On some spectral properties of operators generated by quasi-differential multi-interval systems. (English) Zbl 1078.34066
Summary: We construct the common and the ordered spectral representation for operators, generated as direct sums of selfadjoint extensions of quasi-differential minimal operators on a multi-interval set (selfadjoint vector-operators), acting in a Hilbert space. The structure of the ordered representation is investigated for the case of differential coordinate operators. Results, connected with other spectral properties of such vector-operators, such as the introduction of the identity resolution and the spectral multiplicity are obtained, too.

34L05 General spectral theory of ordinary differential operators
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
47A10 Spectrum, resolvent
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
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