3 papers
math.FA2024
Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
Eva-Maria Hekkelman, Edward McDonald, Teun D. H. van Nuland
We push the definition of multiple operator integrals (MOIs) into the realm of unbounded operators, using the pseudodifferential calculus from the works of Connes and Moscovici, Hi…
math.FA2023
Nonlinear partial differential equations on noncommutative Euclidean spaces
Edward McDonald
Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress i…
math.FA2022
Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups
Zhijie Fan, Ji Li, Edward McDonald +2
Along the line of singular value estimates for commutators by Rochberg-Semmes, Lord-McDonald-Sukochev-Zanin and Fan-Lacey-Li, we establish the endpoint weak Schatten class estimate…