6 papers · 1 filter
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…
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…
Mapping properties of operator-valued pseudo-differential operators
Runlian Xia, Xiao Xiong
In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued…
Operator-valued Triebel-Lizorkin spaces
Runlian Xia, Xiao Xiong
This paper is devoted to the study of operator-valued Triebel-Lizorkin spaces. We develop some Fourier multiplier theorems for square functions as our main tool, and then study the…
Noncommutative harmonic analysis on semigroup and ultracontractivity
Xiao Xiong
We extend some classical results of Cowling and Meda to the noncommutative setting. Let be a symmetric contraction semigroup on a noncommutative space $L_p(\mathcal{M…