| Mean Bounded Variation Condition and Applications in Fourier Analysis |
| Received:December 22, 2006 Revised:March 26, 2007 |
| Key Words:
MVBVS trigonometric series convergence integrability best approximation.
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| Fund Project:Open Funds of State Key Laboratory of Oil and Gas Reservoir and Exploitation of Southwest Petroleum University (No.PCN0613); NSERC of Canada; the NSERC RCD grant and AARMS of Cananda. |
| Author Name | Affiliation | | ZHOU Song Ping | Institute of Mathematics, Zhejiang Sci-Tech University, Zhejiang 310018, China | | ZHOU Ping | Department of Mathematics, Statistics and Computer Science, St. Francis University, Antigonish Nova Scotia Canada, B2G 2W5 | | YU Dan Sheng | Department of Mathematics, Statistics and Computer Science, St. Francis University, Antigonish Nova Scotia Canada, B2G 2W5 |
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| Abstract: |
| This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier (trigonometric) coefficient sequences. We prove this condition cannot be weakened any further to guarantee the uniform convergence of the sine series. Some interesting and important classical results in Fourier analysis are re-established under this ultimate condition. Over ninty year research history is surveyed in this announcement.The first original paper of this series of papers is posted in arXiv:math.CA/0611805 v1, November 27, 2006. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.04.002 |
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