• DOI:10.1093/IMRN/RNX077
• Corpus ID: 119157508

Singular Values of Weighted Composition Operators and Second Quantization

@article{Putinar2016SingularVO,
  title={Singular Values of Weighted Composition Operators and Second Quantization},
  author={Mihai Putinar and James E. Tener},
  journal={International Mathematics Research Notices},
  year={2016},
  volume={2018},
  pages={6426-6441}
}

• M. Putinar, James E. Tener
• Published 12 December 2016
• Mathematics
• International Mathematics Research Notices

We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal field theory, we establish bounds on the singular values (approximation numbers) of these weighted composition operators. As a byproduct we obtain estimates on the singular values of the restriction operator (embedding operator) $H^2(V) \to H^2(U)$ when $U \subset V$ and the boundary of $U$ touches that of $V$. Moreover, using the connection between the weighted composition operators and restriction operators, we show that these operators exhibit an analog of the Fisher-Micchelli phenomenon for non-compact operators.