Geodesic
A~generalization of the Beurling--Lax theorem
Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 362-368.

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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 $$ \|f\|:=\sup_{-\pi/2\varphi\pi/2}\biggl\{\,\int_0^{+\infty}|f(re^{i\varphi})|^2e^{-2r\sigma|\sin\varphi|}\,dr\biggr\}^{1/2}+\infty. $$ 
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B. V. Vinnitskii; V. N. Dil'nyi. A~generalization of the Beurling--Lax theorem. Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 362-368. http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a3/

[1] Laks P., Fillips R., Teoriya rasseyaniya dlya avtomorfnykh funktsii, Mir, M., 1979

[2] Sedletskii A. M., “Ekvivalentnoe opredelenie prostranstv $H^p$ v poluploskosti i nekotorye prilozheniya”, Matem. sb., 96:1 (1975), 75–82

[3] Titchmarsh E., Vvedenie v teoriyu integralov Fure, Gostekhizdat, M.–L., 1948

[4] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[5] Vinnitskii B. V., “O nulyakh funktsii, analiticheskikh v poluploskosti, i polnote sistem eksponent”, Ukr. matem. zh., 46:5 (1994), 484–500 | MR

[6] Vinnitskii B. V., “Pro rozv"yazki odnoridnogo rivnyannya zgortki v odnomu klasi funktsii, analitichnikh u pivsmuzi”, Matem. studii, 7:1 (1997), 41–52 | MR | Zbl

[7] Fedorov M. A., Grishin A. F., “Some questions of the Nevanlinna theory for the complex half-plane”, Math. Phys. Anal. Geom., 1 (1998), 223–271 | Zbl

[8] Vinnitskii B. V., “Pro uzagalnennya teoremi Peli–Vinera”, Matem. studii, 4:1 (1995), 37–44 | MR | Zbl

[9] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Nauka, M., 1984 | MR | Zbl

[10] Gofman K., Banakhovy prostranstva analiticheskikh funktsii, IL, M., 1963

[11] Vinnitskii B. V., Dilnii V. M., “Pro neobkhidni umovi isnuvannya rozv'yazkiv odnogo rivnyannya tipu zgortki”, Matem. studii, 16:1 (2001), 61–70 | MR

[12] Vynnyts'kyi B. V., Sharan V. L., “On the factorisation of one class of functions analytic in the half-plane”, Matem. studii, 14:1 (2000), 41–48 | MR

[13] Vynnyts'kyi B. V., Dil'nyi V. M., “On solutions of homogeneous convolution equation generated by singularity”, Matem. studii, 19:2 (2003), 149–155 | MR