26 citations · 81 across the 20 of their papers we have counts for
22 papers
Weyl's laws and Connes' Trace Theorem for operator-valued pseudo-differential operators
Edward McDonald, Xiao Xiong, Xinyu Zhang
We investigate the spectral asymptotic behavior of operator-valued classical pseudo-differential operators (DOs) for negative order with symbols taking values in a semifinite vo…
Weyl asymptotic formulas in the nilpotent Lie group setting
Shiqi Liu, Edward McDonald, Fedor Sukochev +1
The asymptotic properties of negative order pseudo-differential operators have been an important part of the spectral theory since H.Weyl's classical results. In this paper, we der…
Schur bounded patterns, submajorisation and operator Lipschitz functions
Edward McDonald, Fedor Sukochev, Dmitriy Zanin
A Schur bounded pattern is a subset such that Schur multiplication by every bounded function on supported on defines a bounded linear ope…
Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global
Shiqi Liu, Edward McDonald, Fedor Sukochev +1
On graded Lie groups, we develop a mechanism that transfers the uniformity of maximal hypoellipcity from the frozen coefficients principal part of a differential operator to the fu…
Calderón's commutator on Stratified Lie groups
Yanping Chen, Zhenbing Gong, Ji Li +2
Motivated by the recent work of Gimperlein and Goffeng on Calderón's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the…
A General Dixmier Trace Formula for the Density of States on Open Manifolds
Eva-Maria Hekkelman, Edward McDonald
We give an abstract formulation of the Dixmier trace formula for the density of states. This recovers prior versions and allows us to provide a Dixmier trace formula for the densit…