On <i>L</i><sup>1</sup>-Convergence of Fourier Series under the MVBV Condition
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Bibliographic record
Abstract
Abstract Let f ∈ L 2π be a real-valued even function with its Fourier series , and let Sn ( f , x ), n ≥ 1, be the n -th partial sum of the Fourier series. It is well known that if the nonnegative sequence ﹛ a n ﹜ is decreasing and lim n →∞ a n = 0, then We weaken the monotone condition in this classical result to the so-called mean value bounded variation (MVBV) condition. The generalization of the above classical result in real-valued function space is presented as a special case of the main result in this paper, which gives the L 1 -convergence of a function f ∈ L 2π in complex space. We also give results on L 1 -approximation of a function f ∈ L 2π under the MVBV condition.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.018 | 0.002 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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