Eigenfunction expansion for the three-dimensional Dirac operator (Q1969981)

For any selfadjoint Dirac operator with discrete spectrum defined on a three-dimensional domain the following theorems are shown. For any \(f\) with compact support, the spectral expansion of f converges locally uniformly or respectively the partial sum converge to f uniformly, if \(f=0\) on a subdomain of the compact support, then the partial sum converge to zero locally uniformly in the subdomain under the assumption that \(f \in L^{b}\) with \(b>1\). For \(b>3/2\) it is proven that the spectral expansion of \(f\) converges to \(f\) absolutely and locally uniformly. This statements are similar to results for Laplace and Schrödinger operators which are discussed in different other works.