This article is cited in 7 papers

A generalization of the Beurling–Lax theorem

B. V. Vinnitskii, V. N. Dil'nyi

Ivan Franko National University of L'viv

Abstract: We obtain conditions for the completeness of the system $\{G(z)e^{\tau z},\tau\leqslant0\}$ in the space $H^2_\sigma(\mathbb C_+)$, $0<\sigma<+\infty$, of functions analytic in the right-hand half-plane for which
$$ \|f\|:=\sup_{-\pi/2<\varphi<\pi/2}\biggl\{\,\int_0^{+\infty}|f(re^{i\varphi})|^2e^{-2r\sigma|\sin\varphi|}\,dr\biggr\}^{1/2}<+\infty. $$


UDC: 517.1

Received: 27.10.2004
Revised: 21.06.2005

DOI: 10.4213/mzm2706

 English version: Mathematical Notes, 2006, 79:3, 335–341

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