In the present paper, we discuss some properties of piecewise linear spectral sequences introduced by Liu and Xu. We have a study on the pointwise and almost everywhere convergence of its corresponding series. Also, i...In the present paper, we discuss some properties of piecewise linear spectral sequences introduced by Liu and Xu. We have a study on the pointwise and almost everywhere convergence of its corresponding series. Also, it is shown that the set G constructed from piecewise linear spectral sequences are bases, but not unconditional bases, for LP（0, 1） where 1 〈 p 〈 ∞, p ≠2.展开更多
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. Moreo...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.展开更多
We consider a theory of noncommutative Gröbner bases on decreasingly filtered alge-bras whose associated graded algebras are commutative.We transfer many algorithms that use commutative Gröbner bases to this...We consider a theory of noncommutative Gröbner bases on decreasingly filtered alge-bras whose associated graded algebras are commutative.We transfer many algorithms that use commutative Gröbner bases to this context.As a result,we have a very effi-cient way to compute Ext groups for a large class of graded algebras.This has many applications especially in algebraic topology.展开更多
基金Supported by Prof.Y.Xu under his grant in program of"One Hundred Distingulshed Chi-nese Scientists"of the Chinese Academy of Sciences,the NNSF(10371122)of China and Poetgraduate Innovation Fund of Chinese Academy of Sciences.
文摘In the present paper, we discuss some properties of piecewise linear spectral sequences introduced by Liu and Xu. We have a study on the pointwise and almost everywhere convergence of its corresponding series. Also, it is shown that the set G constructed from piecewise linear spectral sequences are bases, but not unconditional bases, for LP（0, 1） where 1 〈 p 〈 ∞, p ≠2.
基金supported by Science and Technology Research Project of Jilin Provincial Department of Education of China (Grant No. 2011175)supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11126149),supported by National Natural Science Foundation of China (Grant Nos. 11071250 and 11271162)Guangdong Provincial Government of China through the "Computational Science Innovative Research Team" program
文摘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.
基金supported by China Postdoctoral Science Foundation 2021TQ0015the Fundamental Research Funds for the Central Universities,Peking University。
文摘We consider a theory of noncommutative Gröbner bases on decreasingly filtered alge-bras whose associated graded algebras are commutative.We transfer many algorithms that use commutative Gröbner bases to this context.As a result,we have a very effi-cient way to compute Ext groups for a large class of graded algebras.This has many applications especially in algebraic topology.
