Quaternionic metamonogenic functions in the unit disk

Abstract

We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+λ)$ for diverse $\lambda$) in the unit disk, such that every metamonogenic function is approximable in the quaternionic Hilbert module $L^2$ of the disk. The set is orthogonal except for the small subspace of elements of orders zero and one. These functions are used to express time-dependent solutions of the imaginary-time wave equation in the polar coordinate system.

References in corpus (1)

• Reduced-quaternionic Mathieu functions, time-dependent Moisil-Teodorescu operators, and the imaginary-time wave equation