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...

let h be an infinite--dimensional hilbert space and k(h) be the set of all compact operators on h. we will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher jordan derivation on k(h) associated with the following cauchy-jencen type functional equation 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).

We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model operators for both situations, linear fractional transformations for Herglotz operators, results on Friedrichs and Krein extensions, and realization theorems for cla...

This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl asymptotics for the eigenvalues of non-self-adjoint operators with small random perturbations. In the introduction we also review the notion of pseudo-spectrum ...