Approximation of Functions on Rays in  by Solutions to Convolution Equations

This is a first study of approximation of continuous functions on rays in 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...

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Bibliographic Details
Published in:Siberian mathematical journal 2023, Vol.64 (1), p.48-55
Main Authors: Volchkov, V. V., Volchkov, Vit. V.
Format: Article
Language:English
Subjects:
Approximation
Continuity (mathematics)
Convolution
Entire functions
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:This is a first study of approximation of continuous functions on rays in 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 .
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446623010056