Perfect Discretizations of Differential Operators

Difference-differential operators for basic adaptive discretizations and their central function systems

*Correspondence: [email protected] 3Department of Mathematics, Technische Universität München, Boltzmannstraße 3, Garching, 85747, Germany 4Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova Ulica 2, Maribor, 2000, Slovenia Full list of author information is available at the end of the article Abstract The concept of inherited orthogonality is motivated and a...

The Perfect Laplace Operator for Non-Trivial Boundaries

In Lattice QCD, the perfect action provides a discrete formulation of the theory which is free from lattice artifacts [1]. Few attempts have so far been made to examine perfect discretizations also for classical problems like the numerical solution of differential equations [2–4]. We present an exploratory study of a perfect differential operator in presence of non-trivial boundary condiations,...

Weighted composition operators on measurable differential‎ ‎form spaces

In this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Quadruple and octuple layer potentials in two dimensions I: Analytical apparatus

A detailed analysis is presented of all pseudo-differential operators of orders up to 2 encountered in classical potential theory in two dimensions. Each of the operators under investigation turns out to be a sum of one or more of standard operators (second derivative, derivative of the Hilbert transform, etc.), and an integral operator with smooth kernel. This classification leads to an extrem...