Global Pseudo-differential Operators on the Quantum Group $S{U}_q(2)$

Abstract

In this paper, following [1], we develop the theory of global pseudo-differential operators defined on the quantum group $S{U}_q(2)$, and provide some spectral results concerning these operators. We define a graduation for this algebra of pseudo-differential operators in terms of its natural Fourier decomposition and, using the infinite-dimensional representations introduced by Woronowicz [15], we also provide a $\ast$-representation of $S{U}_q(2)$ as bounded pseudo-differential operators acting on $L^2({\mathbb{S}}^1)$.

from PhD Research Thesis