This article considers the relation between spanning properties of lattice orbits discrete series representations and associated co-volume. The focus is on density theorem, which provides a trichotomy characterizing existence cyclic vectors separating vectors, frames Riesz sequences. We provide an elementary exposition that based solely basic tools from harmonic analysis, representation theory,...

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...