Abstract
For the spaces Ep(Dn) of functions, defined on the Cartesian product of convex polygons, it is established that a system of exponentials of a special type forms a basis. The dependence of the exponents on the vertices of the polygons is indicated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. M. Sedletskii, “Bases of exponentials in the Ep spaces on convex polygons,” Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 5, 1101–1119 (1978).
Yu. I. Melnik, “On Dirichlet series of functions that are regular in convex polygons,” Ukr. Mat. Zh.,32, No. 6, 837–841 (1980).
Yu. I. Mel'nik, “Some properties of series of exponentials representing functions that are regular in convex polygons,” in: Some Problems in the Theory of Approximation of Functions [in Russian], Akad. Nauk UkrSSR, Kiev (1985), pp. 69–81.
A. F. Leont'ev, Exponential Series [in Russian], Nauka, Moscow (1976).
W. Rudin, Functions Theory in Polydiscs, Benjamin, New York (1969).
A. F. Leont'ev, “On the representation of an analytic function in the form of the sum of periodic functions,” Mat. Sb.,93 (135), No. 4, 512–528 (1974).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 324–332, March, 1990.
Rights and permissions
About this article
Cite this article
Ibragimov, G.I. Bases of exponentials in the spaces Ep(Dn) on a poly-polygon and the representation of the functions from this class in the form of sums of periodic functions. Ukr Math J 42, 289–296 (1990). https://doi.org/10.1007/BF01057011
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01057011