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...

Abstract We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures diagonally dominant J -self-adjoint operator matrices. These are used the proof of central result, a theorem -non-negative operators. The applied to singular indefinite Sturm-Liouville with $$L^p$$ ...

Examples of symmetric quantum semimartingales are easy to find, but essentially self-adjoint quantum semimartingales have, in general, proved elusive. This is not unexpected since a quantum semimartingale is in some sense an indefinite integral of a family of unbounded operators, and strong conditions are required to ensure that the sum of even two unbounded self-adjoint operators is self-adjoi...

We consider the long standing open question on whether one can actually compute spectra and pseudospectra of arbitrary (possibly non-self-adjoint) Schrödinger operators.We conclude that the answer is affirmative for “almost all” such operators, meaning that the operators must satisfy rather weak conditions such as the spectrum cannot be empty nor the whole plane. We include algorithms for the g...

In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamil...

We prove that non-self-adjoint harmonic and anharmonic oscillator operators have non-trivial pseudospectra. As a consequence, the computation of high energy resonances by the dilation analyticity technique is not numerically stable.

We provide a comprehensive analysis of matrix-valued Herglotz functions and illustrate their applications in the spectral theory of self-adjoint Hamiltonian systems including matrix-valued Schrödinger and Dirac-type operators. Special emphasis is devoted to appropriate matrix-valued extensions of the well-known Aronszajn-Donoghue theory concerning support properties of measures in their Nevanli...

The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by q-deformation. Simultaneously, angular momentum is deformed to soq(3), it acts on the q-Euclidean space that becomes a soq(3)-module algebra this way. In this paper it is shown, that this algebra can be realized by differential operators acting on C∞ functions on R. On...