Complimentary information using in the task of averaging operators inversion in function space

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The dual task of integral geometry – to define for a given averaging operator the function class where inversion of that operator is possible – is solved. Those classes are defined ambiguously. Full description of those classes is given in the form of minimal complimentary information necessary to know about the function. The possible to give a constructive description of the class is researched and in the case of a finite averaging system the inversion formulas are given.

Keywords: integral geometry, functional space, inversion formula
Citation in English: Koganov A.V. Complimentary information using in the task of averaging operators inversion in function space // Computer Research and Modeling, 2011, vol. 3, no. 3, pp. 241-254
Citation in English: Koganov A.V. Complimentary information using in the task of averaging operators inversion in function space // Computer Research and Modeling, 2011, vol. 3, no. 3, pp. 241-254
DOI: 10.20537/2076-7633-2011-3-3-241-254

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