On the spectra of first order irregular operator equations

The distribution of the spectrum of the operator in the complex plane is studied. The operator is the closure in of the operator originally defined on smooth functions satisfying the condition , where , , , is a model operator in a Hilbert space and . Conditions (criteria) in terms of the parameter ensuring that the eigenfunctions of the operator make up a complete system, a minimal system, or a (Riesz) basis in the Hilbert space are obtained.

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