Interpolation Problem with Knots on a Line for Solutions of a Multidimensional Convolution Equation

We study an interpolation problem with knots on a straight line for solutions of a multidimensional convolution equation of the form , where is a given radial distribution with compact support. The case is considered when the set of interpolation knots is quite rare (the distance between neighboring...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023-08, Vol.44 (8), p.3630-3639
Main Authors: Volchkov, V. V., Volchkov, Vit. V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Convolution
Geometry
Interpolation
Knots
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Radial distribution
Straight lines
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Summary:We study an interpolation problem with knots on a straight line for solutions of a multidimensional convolution equation of the form , where is a given radial distribution with compact support. The case is considered when the set of interpolation knots is quite rare (the distance between neighboring knots tends to infinity as their numbers increase). In this case, a criterion for the solvability of the interpolation problem in the class of solutions of tempered growth is obtained. It is shown that for the existence of such a solution it is necessary and sufficient that the set of positive zeros of the spherical transform of the distribution be nonempty.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223080590