On Best Convergence of Series in the Systems $\varphi(nx)$

A. I. Rubinshtein


Abstract: Sufficient conditions for the best convergence in $L_p$ of series in systems $\varphi(nx)$, where $\varphi(x)$ are polynomials or series in trigonometric and Walsh systems, are obtained.

Keywords: best convergence, trigonometric series, Walsh series, Paley series, Banach space.

UDC: 517.518

Received: 21.03.2015

DOI: 10.4213/mzm10826

 English version: Mathematical Notes, 2015, 98:4, 631–635

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