Hilbert Space Of Vector-functions Research Articles

On Some Class of Normal Differential Operators for First Order

In this work, we construct the minimal and maximal operators generated by linear differential-operator expression for first order in the Hilbert space of vector-functions on finite symmetric interval. Then, deficiency indices of the minimal operator will be calculated and the space of boundary values of this operator will be constructed. By using of Calkin-Gorbachuk method, the general representation of all normal extensions of the formally normal minimal operator in terms of boundary values will also be established. Moreover we explore the spectrum structure of these extensions.

First order maximally dissipative singular differential operators

In this paper, using the Calkin-Gorbachuk method, the general form of all maximal dissipative extensions of the minimal operator generated by first order linear multipoint symmetric singular differential-operator expression in the direct sum of Hilbert space of vector-functions has been found. Later on, the structure of spectrum of these extensions is researched. Finally, the results are supported by an application.

Dissipative canonical type differential operators for first order

In this paper, using the Calkin-Gorbachuk method, the general form of all maximally dissipative extensions of the minimal operator generated by the first order linear symmetric canonical type quasi-differential expression in the weighted Hilbert space of vector functions has been found. Also, the spectrum set of these extensions has been investigated.

Degenerate maximal hyponormal differential operators for the first order

In this study, all maximal hyponormal extensions are given for the degenerate first order in the Hilbert space of vector-functions on a finite interval. The extensions are defined in terms of the boundary values. The structure of the spectrum of the maximal hyponormal extensions is also investigated.

Boundedly solvable degenerate differential operators for first order

Using the methods of operator theory all boundedly solvable extensions of the minimal operator generated by degenerated type differential-operators expression in the weighted Hilbert space of vector-functions in finite interval in terms of boundary conditions. Later on, the structure of spectrum of these type extensions will be investigated.

SELFADJOINT SINGULAR DIFFERENTIAL OPERATORS FOR FIRST ORDER

The parametrization of all selfadjoint extensions of the minimal operator generated by frst order linear symmetric singular differential-operator expression in the Hilbert space of vector-functions defined at the right semi-axis has been given. To this end we use the Calkin-Gorbachuk method. Finally, the structure of spectrum set of such extensions is researched

Solvability of first order functional differential operators

By using the methods of operator theory, all boundedly solvable extensions of minimal operator generated by first order functional differential-operator expression in the Hilbert space of vector-functions on finite interval have been described. The operator framework is also applied to the study of structure of spectrums of these extensions. Applications of obtained results to the concrete models are illustrated.

Maximal sectorial differential operators for first order

In this study, the maximal sectorial linear relations are described. Then, the discreteness of the spectrum of the linear maximal sectorial operators and asymptotical behavior of the eigenvalues of such operators in terms of the eigenvalues of its real part are investigated. Moreover, one result for the differential operators for first order in the Hilbert space of vector functions in finite interval is obtained.

Spectrums of Solvable Pantograph Differential-Operators for First Order

By using the methods of operator theory, all solvable extensions of minimal operator generated by first order pantograph-type delay differential-operator expression in the Hilbert space of vector-functions on finite interval have been considered. As a result, the exact formula for the spectrums of these extensions is presented. Applications of obtained results to the concrete models are illustrated.

Hyponormal differential operators with discrete spectrum

In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.

Multipoint normal differential operators of first order

In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.

Compact inverses of first-order normal differential operators

In this work, firstly we describe all normal extensions of a minimal operator generated by linear differential-operator expression of first order in the Hilbert space of vector functions in finite interval. Later on, we investigate discreteness of spectrum and asymptotical behavior of s-numbers of the inverses of these normal extensions.