Abstract
Let be an arbitrary bounded convex domain in the plane . For a certain sequence of convex functions , , given on the space is constructed as the projective limit of the normed spaces where is the space of analytic functions on . The space is described in terms of Laplace transforms. A special role in this description is played by a generalization, proved in the article, of the Paley-Wiener theorem to the case of spaces of infinitely differentiable functions with prescribed growth near the boundary. The result is used in questions involving expansions of functions in Dirichlet series. Figures: 1. Bibliography: 17 titles.
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