This research focuses on the development of a calculus of pseudo-differential operators on the lattice \mathbb{Z}^n, often referred to as pseudo-difference operators. A distinctive feature of this framework is that the associated phase space is compact, leading to symbol classes defined through their behavior with respect to the lattice variable.
Within this setting, she has established results on composition, adjoints, transposes, and parametrices for elliptic operators. Her work also provides criteria for boundedness on \ell^2, weighted \ell^2, and \ell^p spaces, as well as compactness on \ell^p. Connections with toroidal quantization on the torus \mathbb{T}^n are developed, including applications to Schatten class membership on \ell^2(\mathbb{Z}^n).
In addition, her research addresses Fourier integral operators on the lattice, with conditions for \ell^2-boundedness, and applies these analytical tools to obtain estimates for solutions of difference equations on \mathbb{Z}^n. Further results include Gårding and sharp Gårding inequalities, with applications to the unique solvability of parabolic equations on the lattice.