ON SOME SPECTRAL PROPERTIES OF OPERATORS GENERATED BY QUASI-DIFFERENTIAL MULTI-INTERVAL SYSTEMS

We construct the common and the ordered spectral representation for operators, generated as direct sums of self-adjoint extensions of quasi-differential minimal operators on a multiinterval set (self-adjoint 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 have also been obtained.

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