| Abstrakt: |
Let ℱ be the minimal σ-algebra generated by the orthogonal system {ϕ(x)}, defined on the space (X, S, μ) of finite measure. For a certain class of orthonormal systems one proves that for any ℱ-measurable function f(x), which is finite almost everywhere, there exists a series $$\sum\nolimits_{n = 1^a n^\varphi n}^\infty {(x)} $$ which converges absolutely to f(x) almost everywhere. This result represents an extension of a theorem by R. Gundy on the representation of functions by orthogonal series possessing martingale properties. [ABSTRACT FROM AUTHOR] |
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