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Singular values of weighted composition operators and second quantization

Lookup NU author(s): Professor Mihai Putinar



This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).


We study a semigroup of weighted composition oper- ators on the Hardy space of the disk H2(D), and more generally on the Hardy space H2(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) H2(V ) → H2(U) when U ⊂ 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 operator.

Publication metadata

Author(s): Putinar M, Tener J

Publication type: Article

Publication status: Published

Journal: International Mathematics Research Notices

Year: 2018

Volume: 2018

Issue: 20

Pages: 6426-6441

Print publication date: 23/10/2018

Online publication date: 25/04/2017

Acceptance date: 20/03/2017

Date deposited: 15/03/2017

ISSN (print): 1073-7928

ISSN (electronic): 1687-0247

Publisher: Oxford University Press


DOI: 10.1093/imrn/rnx077


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