Ortega Cerdà, JoaquimSeip, Kristian2013-04-082013-04-082012-100021-7670https://hdl.handle.net/2445/34463By theorems of Ferguson and Lacey ($d=2$) and Lacey and Terwilleger ($d>2$), Nehari's theorem is known to hold on the polydisc $\D^d$ for $d>1$, i.e., if $H_\psi$ is a bounded Hankel form on $H^2(\D^d)$ with analytic symbol $\psi$, then there is a function $\varphi$ in $L^\infty(\T^d)$ such that $\psi$ is the Riesz projection of $\varphi$. A method proposed in Helson's last paper is used to show that the constant $C_d$ in the estimate $\|\varphi\|_\infty\le C_d \|H_\psi\|$ grows at least exponentially with $d$; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc.4 p.application/pdfeng(c) The Hebrew University of Jerusalem, 2012Teoria d'operadorsAnàlisi de FourierAnàlisi harmònicaFuncions de diverses variables complexesOperator theoryFourier analysisHarmonic analysisFunctions of several complex variablesinfo:eu-repo/semantics/article6003132013-04-08info:eu-repo/semantics/openAccess