Geodesic
On operators with discontinuous range
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 298-302.

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With the use of operators from approximation function theory we construct integral operators with discontinuous range of values, which make it possible to obtain uniform approximations of continuous functions on the whole interval of their definition. 
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G. V. Khromova. On operators with discontinuous range. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 3, pp. 298-302. http://geodesic.mathdoc.fr/item/ISU_2016_16_3_a6/

[1] Goncharov V. L., The theory of interpolation and approximation of functions, GITL, M., 1954 (in Russian)

[2] Khromova G. V., “The problem of the reconstruction of functions that are given with error”, U.S.S.R. Comput. Math. Math. Phys., 17:5 (1977), 1161–1171 | MR | Zbl

[3] Sendov B. X., “A modified Steklov function”, C. R. Acad. Bulg. Sci., 134:2 (1983), 355–379

[4] Khromov A. P., Khromova G. V., “On a modification of the Steklov operator”, Modern Problems in Function Theory and Applications, Abstracts of Papers of Saratov Winter School, Saratov Univ. Press, Saratov, 2010, 181 (in Russian)

[5] Khromov A. P., Khromova G. V., “A family of operators with discontinuous ranges and approximation and restoration of continuous functions”, Comput. Math. Math. Phys., 53:10 (2013), 1603–1609 | DOI | DOI | MR | Zbl

[6] Khromov A. P., Khromova G. V., “Discontinuous Steklov operators in the problem of uniform approximation of derivatives on an interval”, Comput. Math. Math. Phys., 54:9 (2014), 57–62 | DOI | DOI

[7] Khromov A. A., Khromova G. V., “The solution of the problem of determining the density of heat sources in a rod”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 15:3 (2015), 309–314 | DOI | Zbl

[8] Khromova G. V., “Regularization of Abel Equation with the Use of Discontinuous Steklov Operator”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4 (2014), 597–601

[9] Khromova G. V., “On uniform approximations to the solution of the Abel integral equation”, Comput. Math. Math. Phys., 55:10 (2015), 1703–1712 | DOI | DOI | Zbl

[10] Nathanson I. P., Theory of functions of a real variable, Lan', St. Petersburg, 2013, 560 pp. (in Russian)