On boundedly divergent Walsh-Fourier series
β Scribed by F. Schipp
- Publisher
- Akadmiai Kiad
- Year
- 1990
- Tongue
- English
- Weight
- 272 KB
- Volume
- 56
- Category
- Article
- ISSN
- 1588-2632
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π SIMILAR VOLUMES
An open problem in the theory of Fourier series is whether there are functions f e L1 such that the partial sums S.(f, x) diverge faster than log log n, almost everywhere in x. For a class of particularly 'bad' functions Kahane proved that the rate of divergence is faster than o0og log n). We give h
## Abstract We define the effective integrability of Fineβcomputable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integrals such as the Bounded Convergence Theorem, the Dominated Convergence Theorem, and the Second Mean Value Theorem. It is also proved that th