On approximation properties of one trigonometric system
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 13-25.

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We obtain the criteria of completeness and minimality of a system. We also obtain an analog of the Paley–Wiener theorem related to this system.
Keywords: Paley–Wiener theorem, complete system, minimal system.
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B. V. Vinnitskii; V. N. Dilnyi. On approximation properties of one trigonometric system. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 13-25. http://geodesic.mathdoc.fr/item/IVM_2014_11_a1/

[1] Viner N., Peli R., Preobrazovanie Fure v kompleksnoi oblasti, Nauka, M., 1964 | MR

[2] Vinnitskii B. V., Shavala O. V., “Obmezhenist rozv'yazkiv liniinogo diferentsialnogo rivnyannya drugogo poryadku i odna kraiova zadacha dlya rivnyannya Besselya”, Mat. Stud., 29:3 (2008), 213–216 | MR

[3] Yulmukhametov R. S., Lutsenko V. I., “Obobschenie teoremy Peli–Vinera na vesovye prostranstva”, Matem. zametki, 48:5 (1990), 80–87 | MR | Zbl

[4] Tuan V. K., Zayed A. I., “Paley–Wiener type theorems for a class of integral transform”, J. Math. Anal. Appl., 226:1 (2002), 200–226 | DOI | MR | Zbl

[5] Khabibullin B. N., Polnota sistem eksponent i mnozhestva edinstvennosti, RITs BashGU, Ufa, 2008

[6] Laine I., Nevanlinna theory and complex differential equations, Walter de Gruiter, Berlin, 1993 | MR

[7] Sedletskii A. M., Klassy analiticheskikh preobrazovanii Fure, Fizmatlit, M., 2005

[8] Levin B., Lectures on entire functions, AMS, Providence, RI, 1996 | MR | Zbl

[9] Vynnyts'kyi B. V., Khats' R. V., “Some approximation properties of the systems of Bessel functions of index $-3/2$”, Mat. Stud., 34:2 (2010), 152–159 | MR | Zbl