This article is cited in 2 papers

Convergence and divergence systems

V. F. Gaposhkin


Abstract: A generalization of Carleson's theorem concerning series with respect to systems $\{\varphi(nx)\}$ is proved for the case in which $\varphi(x)$ can be expanded in an absolutely convergent Fourier series. Systems corresponding to functions $\varphi(x)$ which have lacunary Fourier series are studied in detail.

UDC: 517.5

Received: 19.03.1968

 English version: Mathematical Notes, 1968, 4:3, 645–649

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