Properties of expansion systems similar to orthogonal onesстатья
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Аннотация:We define expansion systems in a Hilbert space that are similar to orthogonal ones, for which an analogue of Parseval's equality, the extremal property of expansion coefficients, and analogues of the Riesz-Fischer theorem and Bessel's identity (estimating the accuracy of approximation) are valid. In the case when the Hilbert space is the Lebesgue space L2 we prove an analogue of the Men'shov-Rademacher theorem on almost everywhere convergence and analogues of the theorems of Orlicz and Tandori on unconditional convergence. We suggest constructions and examples of non-orthogonal expansion systems similar to orthogonal ones.