Year: 2026
Type: preprint
Abstract: In this paper, we obtain a complete classification of Toeplitz + Hankel operators on the vector-valued Hardy space $H^2_{\mathcal{E}}(\mathbb{D}^n)$ over the polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$ for $n\geq 1$. We also characterize the paired operators on $L^2(\mathbb{T}^n)$. Furthermore, we give a complete characterization for the class of essentially Toeplitz + essentially Hankel operators on the vector-valued Hardy space $H^2_{\mathcal{E}}(\mathbb{D})$ for finite-dimensional Hilbert space $\mathcal{E}$.
Source: arXiv (Cornell University)
Authors: Babbar, Kritika, Javed, Mo, Maji, Amit
Institution: Indian Institute of Technology Roorkee
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165773335