On the rate of approximation of functions in Lipschitz norms
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 297-299
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We show that the problem on the rate of approximation of functions in Lipschitz norms is reduced to estimating approximations in $C$. Approximations in Lipschitz norms by Vallée Poussin sums are considered as an example.
Keywords: trigonometric polynomials, modulus of continuity, Lipschitz norms
Mots-clés : Vallée Poussin sums.
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S. A. Telyakovskii. On the rate of approximation of functions in Lipschitz norms. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 297-299. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a27/

[1] Prssdorf S., “Zur Konvergenz der Fourierreihen hölderstetiger Funktionen”, Math. Nachr., 69:1 (1975), 7–14 | DOI | MR

[2] Leindler L., Meir A., Totik V., “On approximation of functions in Lipschitz norms”, Acta Math. Hung., 45:3-4 (1985), 441–443 | DOI | MR | Zbl

[3] Stechkin S.B., “O poryadke nailuchshikh priblizhenii nepreryvnykh funktsii”, Izv. AN SSSR. Ser. mat., 15:3 (1951), 219–242 | MR | Zbl

[4] Efimov A.V., “O priblizhenii periodicheskikh funktsii summami Valle-Pussena”, Izv. AN SSSR. Ser. mat., 23:5 (1959), 737–770 | MR | Zbl

[5] Stypinski Z., “On a generalization of the theorem of Prössdorf”, Funct. Approx. Comment. Math., 7 (1979), 101–104 | MR | Zbl

[6] Leindler L., “Generalization of Prössdorf's theorem”, Studia Sci. Math. Hung., 14 (1979), 431–439 | MR | Zbl