Cesàro means of subsequences of partial sums of trigonometric Fourier series. (English) Zbl 1431.42005
The author gives an answer of a question asked by Z. Zalcwasser [Stud. Math. 6, 82–88 (1936; Zbl 0015.25504)] with respect to the trigonometric system: how rare can a sequence of strictly monotone increasing integers \((n_j)\) be such that the almost everywhere relation \(\frac{1}{N}\sum^N_{j=1}S_{nj}f\to f\) is fulfilled for each integrable function \(f\).
Reviewer: Şebnem Yıldız (Kırşehir)
MSC:
| 42A24 | Summability and absolute summability of Fourier and trigonometric series |
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
Keywords:
Cesàro means; subsequences of partial sums; trigonometric Fourier series; a.e. convergence; Zalcwasser’s problemCitations:
Zbl 0015.25504References:
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