Abstract
This is a first study of approximation of continuous functions on rays in \( ^{n} \) by smooth solutions to a multidimensional convolution equation with a radial convolutor. We obtain an analog of the well-known Carleman’s Theorem on tangent approximation by entire functions. As consequences, we give some new results of interest for the theory of convolution equations. These results concern the density in \( \) of the range of some solutions to the convolution equation as well as the possible growth of solutions on rays in \( ^{n} \).
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 1, pp. 56–64. https://doi.org/10.33048/smzh.2023.64.105
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Volchkov, V.V., Volchkov, V.V. Approximation of Functions on Rays in \( ^{n} \) by Solutions to Convolution Equations. Sib Math J 64, 48–55 (2023). https://doi.org/10.1134/S0037446623010056
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DOI: https://doi.org/10.1134/S0037446623010056