A Characterization of Multidimensional Multi-knot Piecewise Linear Spectral Sequence and Its Applications

A Characterization of Multidimensional Multi-knot Piecewise Linear Spectral Sequence and Its Applications

We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 29; no. 9; pp. 1679 - 1690
Main Authors: Cui, Xiao Na, Liu, Xu, Wang, Rui, Yan, Dun Yan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-09-2013
Springer Nature B.V
Subjects:
Applied mathematics
Construction
Convergence
Fourier analysis
Fourier series
Knots
Mathematical functions
Mathematical models
Mathematics
Mathematics and Statistics
Riesz平均
Science
Sequences
Spectra
Spectral lines
Studies
Theorems
傅立叶级数
分段线性
多结
多维
应用
特征
谱序列
Bochner-Riesz means
Spectral sequences
42B35
convergence analysis
42B20
orthonormal exponential bases
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Summary:We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier series.
Bibliography:Xiao Na CUI,Xu LIU,Rui WANG,Dun Yan YAN（School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China;School of Applied Mathematics, Jilin University of Finance and Economies, Changchun 130117, P. R. China;School of Mathematics, Jilin University, Changchun 130012, P. R. China;School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, P. R. China）
Spectral sequences; orthonormal exponential bases; convergence analysis; Bochner-Riesz means
11-2039/O1
We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2（[0,1）d）, which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier series.
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content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-013-2099-y