4 citations · 4 across the 5 of their papers we have counts for
6 papers · 1 filter
Semiclassical Weyl law and exact spectral asymptotics in noncommutative geometry
Edward McDonald, Fedor Sukochev, Dmitriy Zanin
We prove a Tauberian theorem for singular values of noncommuting operators which allows us to prove exact asymptotic formulas in noncommutative geometry at a high degree of general…
Quantum differentiability on quantum tori
Edward McDonald, Fedor Sukochev, Xiao Xiong
We provide a full characterisation of quantum differentiability (in the sense of Connes) on quantum tori. We also prove a quantum integration formula which differs substantially fr…
Quantum differentiability on noncommutative Euclidean spaces
Edward McDonald, Fedor Sukochev, Xiao Xiong
We study the topic of quantum differentiability on quantum Euclidean -dimensional spaces (otherwise known as Moyal -spaces), and we find conditions that are necessary and suf…
Quantum Euclidean Spaces with Noncommutative Derivatives
Li Gao, Marius Junge, Edward McDonald
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean spa…
Noncommutative Geometry for Symmetric Non-Self-Adjoint Operators
Alain Connes, Galina Levitina, Edward McDonald +2
We introduce the notion of a pre-spectral triple, which is a generalisation of a spectral triple where is no longer required to be self-adjoint, but close…
A -algebraic approach to the principal symbol II
Fedor Sukochev, Edward McDonald, Dmitriy Zanin
We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approac…