Geodesic
Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 5-9 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider $(LB)$ spaces of functions which are holomorphic in a convex domain and have a finite type with respect to an order near its boundary. Using Laplace transformation, we give a description of their duals. Then we characterize mimimal absolutely representing systems of exponential functions in these spaces and prove that they always exist. 
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A. V. Abanin; V. A. Varziev. Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 5-9. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a0/

[1] Leontev A. F., “Ryady eksponent dlya funktsii s opredelennym rostom vblizi granitsy”, Izv. AN SSSR. Ser. mat., 44:6 (1980), 1308–1328 | MR | Zbl

[2] Yulmukhametov R. S., “Dostatochnye mnozhestva v odnom klasse prostranstv tselykh funktsii”, Mat. sb., 116(158):3 (1981), 427–439 | MR | Zbl

[3] Napalkov V. V., “Prostranstva analiticheskikh funktsii zadannogo rosta vblizi granitsy”, Izv. AN SSSR. Ser. mat., 51:2 (1987), 287–305 | MR | Zbl

[4] Belghiti T., “Espaces de fonctions holomorphes à poids”, C. R. Acad. Sci. Paris, Ser. I, 318 (1994), 619–622 | MR | Zbl

[5] Abanin A. V., “Netrivialnye razlozheniya nulya i absolyutno predstavlyayuschie sistemy”, Mat. zametki, 57:4 (1995), 483–497 | MR | Zbl

[6] Abanin A. V., Le Hai Khoi, Nalbandyan Yu. S., “Minimal absolutely representing systems of exponentials for $A^{-\infty}(\Omega)$”, J. Approx. Theory, 163 (2011), 1534–1545 | DOI | MR | Zbl

[7] Melikhov S. N., “(DFS)-spaces of holomorphic functions invariant under differentiation”, J. Math. Anal. Appl., 297 (2004), 577–586 | DOI | MR | Zbl

[8] Abanin A. V., Le Hai Khoi, “Dual of the function algebra $A^{-\infty}(D)$ and representation of functions in Dirichlet series”, Proc. Amer. Math. Soc., 138 (2010), 3623–3635 | DOI | MR | Zbl

[9] Bonet J., Braun R. W., Meise R., Taylor B. A., “Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions”, Studia Math., 99 (1991), 155–184 | MR | Zbl

[10] Leontev A. F., Tselye funktsii. Ryady eksponent, Nauka, M., 1983, 176 pp. | MR

[11] Ehrenpreis L., Fourier analysis in several complex variables, Pure and Appl. Math., 17, Wiley-Interscience Publishers, New York, 1970, 506 pp. | MR | Zbl

[12] Korobeinik Yu. F., “Predstavlyayuschie sistemy”, Uspekhi mat. nauk, 36:1 (1981), 73–126 | MR | Zbl

[13] Abanin A. V., Varziev V. A., “Dostatochnye mnozhestva v vesovykh prostranstvakh Freshe tselykh funktsii”, Sib. mat. zhurn. (to appear)

[14] Yulmukhametov R. S., “Priblizhenie subgarmonicheskikh funktsii”, Mat. sb., 124(166):3 (1984), 393–415 | MR | Zbl