Accretive Canonical Type Quasi-Differential Operators for First Order

Abstract

It is known that a linear closed densely defined operator in any Hilbert space   is called accretive if its real part is non-negative and maximal accretive if it is accretive and it does not have any proper accretive extension [1].

Note that the study of abstract extension problems for operators on Hilbert spaces goes at least back to J.von Neumann [2] such that in [2] a full characterization of all selfadjoint extensions of a given closed symmetric operator with equal deficiency indices was investigated.  

Class of accretive operators is an important class of non-selfadjoint operators in the operator theory. Note that spectrum set of the accretive operators lies in right half-plane.

The maximal accretive extensions of the minimal operator generated by regular differential-operator expression in Hilbert space of vector-functions defined in one finite interval case and their spectral analysis have been studied by V. V. Levchuk [3].

In this work, using the method Calkin-Gorbachuk all maximal accretive extensions of the minimal operator generated by linear canonical type quasi-differential operator expression in the weighted Hilbert space of the vector functions defined at right semi-axis are described. Lastly, geometry of spectrum set of these type extensions will be investigated.

Keywords

• Accretive operator,Quasi-differential operator,Spectrum

References

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