We consider the subspace of the Schwartz space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in a multidimensional real space equipped with the topology defined by a countable family of norms constructed with the help of a family of convex separately radial functions in ℝn. We describe the strong dual of this subspace in terms of the Fourier–Laplace transform of functionals.
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Translated from Problemy Matematicheskogo Analiza 112, 2021, pp. 89-104.
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Musin, I.K., Rakhimova, A.I. Paley–Wiener–Schwartz Type Theorem for Ultradistributions on an Unbounded Closed Convex Set. J Math Sci 259, 210–229 (2021). https://doi.org/10.1007/s10958-021-05612-y
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DOI: https://doi.org/10.1007/s10958-021-05612-y