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arXiv · 1612.03970

Singular values of weighted composition operators and second quantization

Mihai Putinar·James E. Tener
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Abstract

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.

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Mihai Putinar, James E. Tener. 2016-12-12. Singular values of weighted composition operators and second quantization. https://arxiv.org/abs/1612.03970

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