This article is cited in 5 papers

On the orthorecursive expansion with respect to a certain function system with computational errors in the coefficients

V. V. Galatenko

M. V. Lomonosov Moscow State University

Abstract: Orthorecursive expansions with computational errors in the coefficients are considered. An example of a system of functions on an interval of the real axis is presented such that the corresponding orthorecursive expansion converges to the expanded element for arbitrary errors satisfying certain rather weak conditions. For various classes of expanded functions results on a.e. convergence, convergence in the $L^p$-metrics ($1\leqslant p<\infty$), and uniform convergence are established.

UDC: 517.518+517.982

MSC: 41A58, 42C15

Received: 20.01.2003 and 04.12.2003

DOI: 10.4213/sm833

 English version: Sbornik: Mathematics, 2004, 195:7, 935–949

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