Geodesic
Fourier transform and quasi-analytic classes of functions of bounded type on tubular domains
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 97-100.

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A condition for a function of bounded type to belong to the Hardy class $H^1$ in terms of the Fourier transform of the boundary values of this function on $R^n$ is found. Applications of the obtained result to the theories of Hardy classes and of quasi-analytic classes of functions are given.
Mots-clés : Fourier transform
Keywords: quasi-analytic classes, pluriharmonic function, tubular domain. 
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F. A. Shamoyan. Fourier transform and quasi-analytic classes of functions of bounded type on tubular domains. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 97-100. http://geodesic.mathdoc.fr/item/FAA_2017_51_2_a10/

[1] Dzh. Garnet, Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR

[2] U. Rudin, Teoriya funktsii v polikruge, Mir, M., 1974 | MR

[3] A. B. Aleksandrov, Kompleksnyi analiz — mnogie peremennye–2, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 8, VINITI, M., 1985, 115–190

[4] V. S. Vladimirov, A. G. Sergeev, Kompleksnyi analiz — mnogie peremennye–2, Itogi nauki i tekhniki. Covremennye problemy matematiki. Fundamentalnye napravleniya, 8, 1985, 191–266

[5] F. A. Shamoyan, Algebra i analiz, 20:4 (2008), 218–240 | MR

[6] F. A. Shamoyan, Sib. matem. zh., 57:6 (2016), 1403–1421 | MR | Zbl

[7] R. B. Salinas, Rev. Acad. Ciencias Madrid, 49 (1955), 331–368 | MR | Zbl

[8] F. A. Shamoyan, Matem. sb., 193:6 (2002), 143–162 | DOI