arXiv subjects

Christopher Benjamin Deng

Publications and source records attributed to Christopher Benjamin Deng.

2 recordsLinked to original sources

arXiv2024

Differential operators on {B}ergman space on bounded symmetric domains

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the $N$-dimensional unit ball $\mathbb{B}^N$ and $\mathbb{D}^2$ of $2\times2$ complex matrices satisfying $I-ZZ^*>0$.Our main tools are the discrete series representations of $\mathrm{SU}(N,1)$ and $\mathrm{SU}(2,2)$. We believe that our observations extend to general bounded symmetric domains.

math.CV↗

arXiv2022

Uncertainty principles and differential operators on the weighted {B}ergman space

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty principles for such operators. Our main tools are the discrete series representations of $\mathrm{SU}(1,1)$. This approach has the promise to generalize to other bounded symmetric domains.

math.CV↗