Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions (Q435171)

The authors consider a one-dimensional Dirac operator with \(L^2\)-potential and subject to regular boundary conditions and prove that it has discrete spectrum. For strictly regular boundary conditions, the spectrum of the free operator is simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, the authors prove the uniform equiconvergence property and pointwise convergence on a closed interval. Analogous results are obtained for regular but not strictly regular boundary conditions.