This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier (trigonometric) coefficient sequences. We prove this condition cannot be weak- ened any further to guarantee the unifor...This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier (trigonometric) coefficient sequences. We prove this condition cannot be weak- ened 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.展开更多
基金Open Funds of State Key Laboratory of Oil and Gas Reservoir and Exploitation of Southwest Petroleum University (No. PCN0613)NSERC of Canadathe NSERC RCD grant and AARMS of Cananda
文摘This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier (trigonometric) coefficient sequences. We prove this condition cannot be weak- ened 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.
