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This article is cited in 7 scientific papers (total 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
$$
\|f\|:=\sup_{-\pi/2<\varphi<\pi/2}\biggl\{\,\int_0^{+\infty}|f(re^{i\varphi})|^2e^{-2r\sigma|\sin\varphi|}\,dr\biggr\}^{1/2}<+\infty.
$$
Received: 27.10.2004 Revised: 21.06.2005
Citation:
B. V. Vinnitskii, V. N. Dil'nyi, “A generalization of the Beurling–Lax theorem”, Mat. Zametki, 79:3 (2006), 362–368; Math. Notes, 79:3 (2006), 335–341
Linking options:
https://www.mathnet.ru/eng/mzm2706https://doi.org/10.4213/mzm2706 https://www.mathnet.ru/eng/mzm/v79/i3/p362
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Abstract page: | 437 | Full-text PDF : | 118 | References: | 64 | First page: | 1 |
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