Deconvolution problem for indicators of segments

  • Volchkova Natalia P., Donetsk National Technical University, 58 Artyom Street, Donetsk 83000, Ukraine
  • Volchkov Vitaly V., Donetsk National University, 24 Universitetskaya Street, Donetsk 83001, Ukraine
Keywords: convolution equations, inversion formulas, two-radii theorem, compactly supported distributions


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 $f\star\mu_1,\dots,f\star\mu_n$ 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 $f\rightarrow(f\star\chi_{r_1},f\star\chi_{r_2})$ in the indicated case.


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How to Cite
Volchkova, N. and Volchkov, V. ( ) “Deconvolution problem for indicators of segments”, Mathematical notes of NEFU, 26(3), pp. 3-14. doi: