We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of P T symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These P T symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase spa...

We give a sufficient condition for the essential self-adjointness of perturbation square magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function not necessarily bounded. allows perturbations that are bounded from below by constant.

Observables in quantum mechanics are represented by self-adjoint operators on Hilbert space. Such ubiquitous, well-known, and very foundational fact, however, is traditionally subtle to be explained typical first classes mechanics, as well senior physicists who have grown up with the lesson that self-adjointness “just technical”. The usual difficulties clarify connection between demand for cert...