For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

We consider a general nonselfadjoint second order scalar operator in planar domain such that one of the boundary components is obtained by an arbitrary irregular curving under assumption amplitude small. The Dirichlet or Neumann condition imposed on perturbed component, and remaining part boundary. prove norm resolvent convergence operators, estimate rate two norms, spectrum operators. In selfa...

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.

Among all linear operators on Hilbert spaces, the compact ones (defined below) are the simplest, and most closely imitate finite-dimensional operator theory. In addition, compact operators are important in practice. We prove a spectral theorem for self-adjoint compact operators, which does not use broader discussions of properties of spectra, only using the Cauchy-Schwarz-Bunyakowsky inequality...

We consider a Sturm-Liouville boundary value problem in a bounded domain D of Rn. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on ∂D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the me...

In this paper several new inequalities of Grüss’ type for Riemann– Stieltjes integral with monotonic nondecreasing integrators under various assumptions for integrands are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well. Department of Mathematics, Faculty of Science, Jerash University, 26150 Jerash, Jordan. E-mail address: mwomath@gmail...