Hankel forms on Fock space modulo \(C_ N\)
The author obtains a boundedness criterion for Hankel forms acting on a subspace of the Fock space \(F^{\alpha}({\mathbb{C}})\), which consists of the entire functions that are square integrable with respect to measure \(\mu\) given by \(d\mu =\exp (-\alpha | z|^ 2)dz.\) This extends earlier work of \textit{S. Janson}, the author and \textit{R. Rochberg} [Rev. Mat. Iberoamericana 3, 61-138 (1988)] in which a theory of Hankel forms on such spaces was first developed. In the present work, the author considers the subspace \(F_ i^{\alpha}\) of functions satisfying \(f(\omega z)=\omega^ if(z)\), where \(\omega\) is a primitive Nth root of unity. He proves that a Hankel form \(\Gamma_ b\) acting on \(F^{\alpha}_ i\times F^{\alpha}_ j\), with symbol b satisfying \(b(\omega z)=\omega^{i+j}f(z)\), is bounded if and only if \(b(z)=O(\exp (\alpha | z|^ 2))\). He also observes that ``presumably similar considerations can be made in higher dimensions''.
scientific article; zbMATH DE number 4180147