Geodesic
Deconvolution problem for indicators of segments
Matematičeskie zametki SVFU, Tome 26 (2019) no. 3, pp. 1-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : convolution equations, inversion formulas
Keywords: two-radii theorem, compactly supported distributions. 
@article{SVFU_2019_26_3_a0,
     author = {N. P. Volchkova and Vit. V. Volchkov},
     title = {Deconvolution problem for indicators of segments},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {1--14},
     year = {2019},
     volume = {26},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2019_26_3_a0/}
}
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N. P. Volchkova; Vit. V. Volchkov. Deconvolution problem for indicators of segments. Matematičeskie zametki SVFU, Tome 26 (2019) no. 3, pp. 1-14. http://geodesic.mathdoc.fr/item/SVFU_2019_26_3_a0/