本文指出文[1]中的定理4.1证明中包含着错误,并且建立了相应的正确结果。设α_0/2+sum from n=1 to ∞ α_n cos nx是f∈L(0,π]的Fourier余弦级数,假如存在a>0和单调数列{l_n}∈SV(N)使得α_n/(n~αl_n)↘(n→∞),那么下面两断言是...本文指出文[1]中的定理4.1证明中包含着错误,并且建立了相应的正确结果。设α_0/2+sum from n=1 to ∞ α_n cos nx是f∈L(0,π]的Fourier余弦级数,假如存在a>0和单调数列{l_n}∈SV(N)使得α_n/(n~αl_n)↘(n→∞),那么下面两断言是等价的,(ⅰ) ‖S_n(f)-f‖_(L1)=0(1)(n→∞):(ⅱ)α_nlogn→0(n→∞)。展开更多
设p_m≥0↓,sum from k=0 to n(p_n)=P_m,n=0,l,…,p_0=P_0=1,P_n→∞(n→∞)若N_n=1/P_n sum from k=0 ton(p_(n,k)S_k→S(n t。0→∞)),则说{S_k}关于算子(N,p_n)收敛于S.设f(x)∈L_(?),S_n(f,x)
Let {q<sub>n</sub>} be monotone decreasing sequence for sufficiently large n. If the limit of q<sub>n</sub> is zero as n→∞, then it is denoted by q<sub>n</sub>↓ O. If there exis...Let {q<sub>n</sub>} be monotone decreasing sequence for sufficiently large n. If the limit of q<sub>n</sub> is zero as n→∞, then it is denoted by q<sub>n</sub>↓ O. If there exists β】0 such that n<sup>-β</sup>q<sub>n</sub>↓O, then the sequence {q<sub>n</sub>} is called a quasi-monotone sequence, which is denoted by q<sub>n</sub>↓↓O.展开更多
文摘本文指出文[1]中的定理4.1证明中包含着错误,并且建立了相应的正确结果。设α_0/2+sum from n=1 to ∞ α_n cos nx是f∈L(0,π]的Fourier余弦级数,假如存在a>0和单调数列{l_n}∈SV(N)使得α_n/(n~αl_n)↘(n→∞),那么下面两断言是等价的,(ⅰ) ‖S_n(f)-f‖_(L1)=0(1)(n→∞):(ⅱ)α_nlogn→0(n→∞)。
文摘设p_m≥0↓,sum from k=0 to n(p_n)=P_m,n=0,l,…,p_0=P_0=1,P_n→∞(n→∞)若N_n=1/P_n sum from k=0 ton(p_(n,k)S_k→S(n t。0→∞)),则说{S_k}关于算子(N,p_n)收敛于S.设f(x)∈L_(?),S_n(f,x)
文摘Let {q<sub>n</sub>} be monotone decreasing sequence for sufficiently large n. If the limit of q<sub>n</sub> is zero as n→∞, then it is denoted by q<sub>n</sub>↓ O. If there exists β】0 such that n<sup>-β</sup>q<sub>n</sub>↓O, then the sequence {q<sub>n</sub>} is called a quasi-monotone sequence, which is denoted by q<sub>n</sub>↓↓O.
