Spectral analysis of Hahn-Dirac system

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

Spectral Analysis of Relativistic Atoms – Dirac Operators with Singular Potentials

This is the first part of a series of two papers, which investigate spectral properties of Dirac operators with singular potentials. We examine various properties of complex dilated Dirac operators. These operators arise in the investigation of resonances using the method of complex dilations. We generalize the spectral analysis of Weder [50] and Šeba [46] to operators with Coulomb type potenti...

A time-splitting spectral scheme for the Maxwell–Dirac system

We present a time-splitting spectral scheme for the Maxwell–Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell– Dirac system conserves the Lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show. In particular, we focus in our ex...

Dirac Operators and Spectral Geometry

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...