| RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng |
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| 作者姓名： | Kunyang Wang Feng Dai |
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| 作者单位： | [1]School of Mathematical Sciences Beijing Normal University Beijing, 100875 P. R. China [2]Department of Mathematical and Statistical Sciences CAB 632 University of Alberta Edmonton, Alberta Canada T6 2G1 |
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| 基金项目： | the International Symposium on Approximation Theory and Remote Sensing Applications held in Kunming, China
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国家自然科学基金
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the NSERCCanada |
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| 摘 要： | As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.
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| 关 键 词： | 球谐逼近 北京师范大学研究组 研究进展 傅立叶-拉普拉斯膨胀 光滑度 孙永生教授 |
| 收稿时间： | 2006-10-28 |
Recent progress on spherical harmonic approximation made by BNU research group |
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| Kunyang Wang Feng Dai.Recent progress on spherical harmonic approximation made by BNU research group[J].Analysis in Theory and Applications,2007,23(1):50-63. |
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| Authors: | Kunyang Wang Feng Dai |
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| Institution: | (1) School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China;(2) Department of Mathematical and Statistical Sciences CAB 632, University of Alberta, Edmonton, Alberta, Canada, T6 2G1 |
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| Abstract: | As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005).Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths. |
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| Keywords: | spherical harmonics Fourier-Laplace expansion convergence approximation smoothness K-functional width memory RESEARCH HARMONIC APPROXIMATION SPHERICAL PROGRESS linear smoothness series achievements area group relative during recent paper guidance spherical harmonic analysis approximation students |
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