Peculiarities of the partial Fourier-Haar sum behavior at dyadic irrational discontinuity points. (English. Russian original) Zbl 1282.42027
Sib. Math. J. 54, No. 6, 1059-1063 (2013); translation from Sib. Mat. Zh. 54, No. 6, 1331-1336 (2013).
Summary: We obtain an exact description for the behavior of Fourier-Haar sums at dyadic irrational discontinuity points for functions of bounded variation.
MSC:
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
References:
| [1] | Kashin B. S. and Saakyan A. A., Orthogonal Series, Amer. Math. Soc., Providence (1999). · Zbl 1188.42010 |
| [2] | Golubov B. I., ”Fourier series by the Haar system,” in: Mathematical Analysis [in Russian], VINITI, Moscow, 1971, pp. 109–146 (Itogi Nauki i Tekhniki). |
| [3] | Ul’yanov P. L., ”On Haar series,” Mat. Sb., 63, No. 3, 356–391 (1964). |
| [4] | Faber G., ”Über die Orthogonalfunktionen des Herrn Haar,” Deutsche Math.-Verl., Bd 19, 104–112 (1910). · JFM 41.0470.01 |
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