A generalization of the Beurling--Lax theorem
The authors obtain conditions for the completeness of the system \(\{G(z)e^{\tau z},\tau\leq 0\}\) in the space \(H^2_\sigma(\mathbb{C}_+)\), \(0< \sigma<+\infty\), of functions analytic in the right-hand half-plane with the norm \[ \|f\|:=\sup_{-\pi/2<\varphi<\pi/2}\left\{\int^{+\infty}_0|f (re^{i\varphi})|^2e^{-2r\sigma|\sin\varphi|}dr \right\}^{1/2}<+ \infty. \]
scientific article; zbMATH DE number 5155459