ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 40, 42 Ziza, O. A., Moscow State Inst. of Electronics and Mathematics, Russia On absolute summability of orthogonal series. Let ∑ c_{n}f_{n}(x) be an orthogonal series (OS) in L^{2}[0, 1]. It is called summable at the point x by the method |SF^{∗}, φ, λ|, where φ = φ(t), t ∈ [0, 1], varphi(0) = 1, φ(1) = 0, and λ = {λ_{n}}, 0 ≤ λ_{n} ↑ ∞, if ∑ |σ_{ν+1}(x) − σ_{ν}(x)| < ∞, σ_{ν}(x) = ∑ c_{n}f_{n}(x)φ(λ_{n}λ_{ν+1}^{−1}). We present necessary and sufficient conditions for |SF^{∗}, φ, λ|summability (in particular by Riesz methods) of OS a. e. References: O. A. Ziza, 1)On absolute summability of orthogonal series, Acta Sci. Math. (Szeged), 2)Summability of Orthogonal series (a monograph, in preparation)