515 Analysis
The classes of band-dominated operators and the subclass of operators in the Wiener algebra W are known to be inverse closed. This paper studies and extends partially known results of that type for one-sided and generalized invertibility. Furthermore, for the operators in the Wiener algebra W invertibility, the Fredholm property and the Fredholm index are known to be independent of the underlying space lp, 1≤p≤∞. Here this is completed by the observation that even the kernel and a suitable direct complement of the range as well as generalized inverses of operators in W are invariant w.r.t. p.
[Mathematische Symbole nur unzureichend darstellbar.]
This paper presents numerical analysis of the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice. Additionally, to provide estimates in interior and exterior domains, two different regularisations of the discrete fundamental solution are considered. Estimates for the absolute difference and lp‐estimates are constructed for both regularisations. Thus, this work extends the classical results in the discrete potential theory to the case of a rectangular lattice and serves as a basis for future convergence analysis of the method of discrete potentials on rectangular lattices.
