4 papers
Connes' trace theorem and the log-polyhomogeneous calculus for Carnot manifolds
Edward McDonald
The Wodzicki residue is the unique trace on the algebra of classical pseudodifferential operators on a closed manifold, and Connes in 1988 proved that it coincides with the Dixmier…
Fujita exponents on quantum Euclidean spaces
Edward McDonald, Michael Ruzhansky, Serikbol Shaimardan +1
We study the well-posedness of a non-linear heat equation with power nonlinearity with positive initial data on quantum Euclidean spaces. We prove a noncommutative analogue of the…
estimates in the Androulidakis-Mohsen-Yuncken calculus
Edward McDonald
We prove that order zero operators in the pseudodifferential calculus associated to a filtration defined by Androulidakis, Mohsen and Yuncken are bounded on spaces for $1<p<\…
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…