Abstract
The author considers the problem of representing functions analytic in a neighborhood of a closed, bounded, convex, multidimensional domain by exponential series (with formulas for the coefficients). In addition, the system of exponents should be the collection of intersection points of the zero planes of a special entire function. A complete description is given of a class of convex domains for which it is possible to solve the problem of representing functions by exponential series in this way.
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