Geodesic
Variation of Fourier–Haar coefficients
Sbornik. Mathematics, Tome 195 (2004) no. 3, pp. 441-457 
V. Sh. Tsagareishvili. Variation of Fourier–Haar coefficients. Sbornik. Mathematics, Tome 195 (2004) no. 3, pp. 441-457. http://geodesic.mathdoc.fr/item/SM_2004_195_3_a5/
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     title = {Variation of {Fourier{\textendash}Haar} coefficients},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Series of differences of Fourier–Haar coefficients are studied. It is demonstrated that in certain cases their behaviour is similar to the behaviour of the series of coefficients themselves.

[1] Haar A., Zur Theorie der orthogonaler Funktionensysteme, Inauguraldissertation, Göttingen, 1909

[2] Haar A., “Zur Theorie der orthogonaler Funktionensysteme”, Math. Ann., 69 (1910), 331–371 | DOI | MR | Zbl

[3] Ulyanov P. L., “Reshenie i peremennye problemy teorii trigonometricheskikh i ortogonalnykh ryadov”, UMN, 19:1 (1964), 3–69 | MR

[4] Ul'yanov P. L., “Haar series and related questions”, A. Haar memorial conference, V. I, II (Budapest, 1985), Colloq. Math. Soc. János Bolyai., 49, North-Holland, Amsterdam, 1987, 57–96 | MR

[5] Ulyanov P. L., “Metricheskaya teoriya funktsii”, Trudy MIAN, 182, 1988, 180–223 | MR

[6] Golubov B. I., “Ryady po sisteme Khaara”, Itogi nauki i tekhniki. Matem. analiz, VINITI, M., 1971, 109–146 | MR

[7] Wade W. R., “Recent developments in the theory of Haar series”, Colloq. Math., 52:2 (1987), 213–238 | MR | Zbl

[8] Aleksich G., Problemy skhodimosti ortogonalnykh ryadov, IL, M., 1963 | MR

[9] Zigmund A., Trigonometricheskie ryady, t. 1, Mir, M., 1965 | MR

[10] Zygmund A., “Smooth functions”, Duke Math. J., 12:1 (1945), 47–75 | DOI | MR

[11] Ulyanov P. L., “O ryadakh po sisteme Khaara”, Dokl. AN SSSR, 149:3 (1963), 532–534 | MR | Zbl

[12] Ulyanov P. L., “O ryadakh po sisteme Khaara”, Matem. sb., 63 (105):3 (1964), 356–391 | MR | Zbl

[13] Golubov B. I., “O ryadakh Fure nepreryvnykh funktsii po sisteme Khaara”, Izv. AN SSSR. Ser. matem., 28:6 (1964), 1271–1296 | MR | Zbl

[14] McLaughlin J. R., “Haar series”, Trans. Amer. Math. Soc., 137 (1969), 153–175 | DOI | MR

[15] Bochkarev S. V., “O koeffitsientakh ryadov po sisteme Khaara”, Matem. sb., 80:1 (1969), 97–116 | MR | Zbl

[16] Stechkin S. B., “Ob absolyutnoi skhodimosti ryadov Fure”, Izv. AN SSSR. Ser. matem., 17 (1953), 87–98 | Zbl