We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in literature such as localization operators, covariant integral quantizations, and quadratic time-frequency representations. In process, we notion of admissibility operators extend well known results to operator setting. A major theme paper is interaction between convolutions, Weyl quantiz...

The fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for computation of relativistic space-charge field. Different to quasi-electrostatic model, our is formulated lab-frame and can be applied without assistance Lorentz transformation. particular, derive a modified admissibility condition which effec...

By discovering that solutions of the vanishing viscosity approximation (but without flux regularization) to a scalar conservation law with discontinuous flux are equal to a flux crossing point at the interface, we derive entropy conditions which provide well-posedness to a corresponding Cauchy problem. We assume that the flux is such that the maximum principle holds, but we allow multiple flux ...

In this paper we study the module contractibility ofBanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. Also weinvestigate module contractibility of Banach algebras with theconcept of the module diagonal.