On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I. General Case
Ключові слова:
operator differential equation, characteristic operator, characteristic projection, solution of Weyl type, maximal semi-definite subspaceАнотація
In the context of dissipative and accumulative differential equations (which contain the spectral parameter $\lambda$ nonlinearly) in a separable Hilbert space $\mathcal{H}$ we introduce a characteristic operator $M(\lambda)$ that works as an analog of the characteristic Weyl-Titchmarsh matrix. Its existence and properties are investigated. A description of $M(\lambda)$ that corresponds to separated boundary conditions is given. Analogs for Weyl functions and solutions are introduced. Weyl type inequalities for those analogs are established, which reduce to well-known inequalities in various special cases. The proofs are based on description and properties of maximal semi-definite subspaces in $\mathcal{H}^2$ of special form that we provide while studying boundary problems for equations as above.
Mathematics Subject Classification: 34A55, 34G10, 47E05.
