Geodesic
Best approximation of the operator of analytic continuation on the class of functions analytic in a strip
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 46-54
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We solve several interrelated extremal problems for the operator of analytic continuation on the class of functions analytic in a strip: the problem of the best approximation of the operator, calculation of its modulus of continuity, and optimal recovery of the operator by inaccurate boundary values of a function on a straight line.
Keywords: approximation of operators, analytic functions in a strip. 
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R. R. Akopyan. Best approximation of the operator of analytic continuation on the class of functions analytic in a strip. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 46-54. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a6/

[1] Arestov V. V., “Priblizhenie neogranichennykh operatorov ogranichennymi i rodstvennye ekstremalnye zadachi”, Uspekhi mat. nauk, 51:6(312) (1996), 89–124 | MR | Zbl

[2] Ibragimov I. I., Teoriya priblizheniya tselymi funktsiyami, Izd-vo Elm, Baku, 1979, 465 pp. | MR | Zbl

[3] Osipenko K. Yu., Optimal recovery of analytic functions, NOVA Science Publ. Inc., Huntington, 2000, 220 pp.

[4] Polia G., Seg G., Zadachi i teoremy iz analiza, v 2 t., v. 1, Nauka, M., 1978, 392 pp.

[5] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M.–L., 1950, 336 pp. | MR

[6] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1981, 799 pp. | MR | Zbl

[7] Stechkin S .B., “Neravenstva mezhdu normami proizvodnykh proizvolnoi funktsii”, Acta Sci. Math., 26:3–4 (1965), 225–230 | Zbl

[8] Stechkin S. B., “Nailuchshee priblizhenie lineinykh operatorov”, Mat. zametki, 1:2 (1967), 137–148 | MR | Zbl