We use C *-algebra theory to provide a new method of decomposing the essential spectra of self-adjoint and non-self-adjoint Schrödinger operators in one or more space dimensions.

Given, on the Hilbert space H0, the self-adjoint operator B and the skew-adjoint operators C1 and C2, we consider, on the Hilbert space H ≃ D(B)⊕H0, the skew-adjoint operator

In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := −[pu∇]∆ + qu, on an arbitrary, bounded time-scale T, for suitable functions p, q, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space L(Tκ), in such a way that the resulting operator is self-adjoint,...

Spectral problem for a self-adjoint third-order differential operator with non-local potential on finite interval is studied. Elementary functions that are analogues of sines and cosines such operators described. Direct inverse problems solved.

In this study, we derive error estimates for time accurate wavelet based schemes in two stages. First we look at the semi-discrete boundary value problem as a Cauchy problem and use spectral decomposition of self adjoint operators to arrive at the temporal error estimates both in L2 and energy norms. Later, following the wavelet approximation theory, we propose spatial error estimates in L2 and...

The use of thin liquid films has expanded beyond lubrication and coatings, into applications in actuators adaptive optical elements. In contrast to their predecessors, whose dynamics can be typically captured by modelling infinite or periodic films, these are characterized a finite amount an impermeable domain. global mass conservation constraint, together with common boundary conditions (e.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 consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism ...