we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from class $W_2^{-1}$ is solved by method of mappings. We prove uniqueness theorem, develop constructive algorithm solution and obtain necessary sufficient conditions solvability in self-adjoint non-self-adjoint cases.

Let AN be the symmetric operator given by the restriction of A toN , where A is a self-adjoint operator on the Hilbert space H and N is a linear dense set which is closed with respect to the graph norm on D(A), the operator domain of A. We show that any self-adjoint extension AΘ of AN such that D(AΘ)∩D(A) = N can be additively decomposed by the sum AΘ = Ā + TΘ, where both the operators Ā and TΘ...

Let A be a bounded self-adjoint operator on a separable Hilbert space H and H0 ⊂ H a closed invariant subspace of A. Assuming that H0 is of codimension 1, we study the variation of the invariant subspace H0 under bounded self-adjoint perturbations V of A that are off-diagonal with respect to the decomposition H = H0 ⊕H1. In particular, we prove the existence of a oneparameter family of dense no...

Let A be a bounded self-adjoint operator on a separable Hilbert space H and H0 ⊂ H a closed invariant subspace of A. Assuming that H0 is of codimension 1, we study the variation of the invariant subspace H0 under bounded self-adjoint perturbations V of A that are off-diagonal with respect to the decomposition H = H0 ⊕ H1. In particular, we prove the existence of a one-parameter family of dense ...