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This article is cited in 2 scientific papers (total in 2 papers)
Mathematics
Deconvolution problem for indicators of segments
N. P. Volchkovaa, Vit. V. Volchkovb a Donetsk National Technical University, 58 Artyom Street, Donetsk 83000, Ukraine
b Donetsk National University, 24 Universitetskaya Street, Donetsk 83001, Ukraine
Abstract:
Let $\mu_1,\dots,\mu_n$ be a family of compactly supported distributions on real axis. Reconstruction of a function (distribution) $f$ by given convolutions $f\ast\mu_1,\dots,f\ast\mu_n$ is called deconvolution. We consider the deconvolution problem for $n=2$ and $\mu_j=\chi_{r_j},$ $j=1,2,$ where $\chi_{r_j}$ is the indicator of segment $[-r_j, r_j].$ This problem is correctly settled only under the condition of incommensurability of numbers $r_1$and $r_2$. The main result of the article gives an inversion formula for the operator
$f\rightarrow(f\ast\chi_{r_1},f\ast\chi_{r_2})$ in the indicated case.
Keywords:
convolution equations, inversion formulas, two-radii theorem, compactly supported distributions.
Received: 21.12.2018 Revised: 04.08.2019 Accepted: 03.09.2019
Citation:
N. P. Volchkova, Vit. V. Volchkov, “Deconvolution problem for indicators of segments”, Mathematical notes of NEFU, 26:3 (2019), 1–14
Linking options:
https://www.mathnet.ru/eng/svfu257 https://www.mathnet.ru/eng/svfu/v26/i3/p1
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