Finite rank Hankel operators over the complex Wiener space (Q1777431)

This paper discusses finite-rank small Hankel operators \(H_{b}\) on a Hilbert space of holomorphic, square integrable Wiener functionals, where \(b\) is called a finite-rank symbol, \(H_{b}\) is continuous and has finite rank. The tool used is the unitary equivalent representation of \(H_{b}\) on the Hilbert space of skeletons. The finite rank property is characterized in terms of a functional equation for the symbol \(b\), which generalizes the well-known equation \(b(z+w)=b(z)b(w)\). Also, polynomial finite-rank symbols are investigated in this paper.