Geodesic
Overlapping transformations for approximation of continuous functions by means of repeated mean Valle Poussin
Daghestan Electronic Mathematical Reports, no. 8 (2017), pp. 70-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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On the basis of trigonometric sums of Fourier $S_n(f,x)$ and classical means of Valle Poussin $$ _1V_{n,m}(f,x)= \frac1n\sum_{l=m}^{m+n-1}S_l(f,x) $$ in this paper, repeated mean Valle Poussin is introduced as follows $$ _2V_{n,m}(f,x)= \frac1n\sum_{k=m}^{m+n-1}{}_1V_{n,k}(f,x), $$ $$ {}_{l+1}V_{n,m}(f,x)= \frac1n\sum_{k=m}^{m+n-1} {}_{l}V_{n,k}(f,x)\quad(l\ge1). $$ On the basis of the mean $_2V_{n,m}(f,x)$ and overlapping transforms, operators that approximate continuous (in general, nonperiodic) functions are constructed and their approximative properties are investigated.
Keywords: the repeated mean Valle Poussin, overlapping transforms, local approximative properties. 
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     author = {I. I. Sharapudinov},
     title = {Overlapping transformations for approximation of continuous functions by means of repeated mean {Valle} {Poussin}},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {70--92},
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     url = {http://geodesic.mathdoc.fr/item/DEMR_2017_8_a7/}
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I. I. Sharapudinov. Overlapping transformations for approximation of continuous functions by means of repeated mean Valle Poussin. Daghestan Electronic Mathematical Reports, no. 8 (2017), pp. 70-92. http://geodesic.mathdoc.fr/item/DEMR_2017_8_a7/

[1] Malvar H.S., Signal processing with lapped transform, Artech House, Boston–London, 1992

[2] Zhuk V.V., Approksimatsiya periodicheskikh funktsii, Leningrad, 1982

[3] Nikolskii S.M., “O nekotorykh metodakh priblizheniya trigonometricheskimi summami”, Izv. AN SSSR. Ser. matem., 4:6 (1940), 509–-520

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

[5] Telyakovskii S.A., “O priblizhenii differentsiruemykh funktsii lineinymi srednimi ikh ryadov Fure”, Izv. AN SSSR. Ser. matem., 24:2 (1960), 213–242

[6] Magomed-Kasumov M.G., “Approksimativnye svoistva klassicheskikh srednikh Valle-Pussena dlya kusochno gladkikh funktsii”, Vestnik Dagestanskogo nauchnogo tsentra RAN, 54 (2014), 5–12

[7] Sharapudinov I.I., “Approksimativnye svoistva srednikh Valle-Pussena na klassakh tipa Soboleva s peremennym pokazatelem”, Vestnik Dagestanskogo nauchnogo tsentra RAN, 2012, no. 45, 5-–13

[8] Sharapudinov I.I., “Priblizhenie gladkikh funktsii v $L_{2\pi}^{p(x)}$ srednimi Valle-Pussena”, Izvestiya Saratovskogo universiteta. Seriya Matematika. Mekhanika. Informatika, 13:1-1 (2012), 45-–49

[9] Sharapudinov I.I., “Priblizhenie funktsii v $L^{p(x)}_{2\pi}$ trigonometricheskimi polinomami”, Izvestiya RAN: Seriya matematicheskaya, 77:2 (2013), 197–-224 | DOI | MR | Zbl

[10] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, Moskva, 1965 | MR