设L是常系数n阶线性微分算子,m∈N, 0=s_0<s_1<…<s_r<s_(r+1)=1是一组自由节点,在s_v处的重数是m_v≥1,sum from v=1 to r m_v≤m。广义样条 Φ~*(m,q)={φ|Lφ=0,φ∈C~∞(s_v,s_(v+1),v=0,1,…,r,且φ∈C^(n-1-qm_v)(s_v...设L是常系数n阶线性微分算子,m∈N, 0=s_0<s_1<…<s_r<s_(r+1)=1是一组自由节点,在s_v处的重数是m_v≥1,sum from v=1 to r m_v≤m。广义样条 Φ~*(m,q)={φ|Lφ=0,φ∈C~∞(s_v,s_(v+1),v=0,1,…,r,且φ∈C^(n-1-qm_v)(s_v-δ,s_v+δ),δ>0适当小,v=1,…,r}本文证明了设f∈L_p[0,1],1≤p<∞,那末当n≥2时,存在f的最佳L_p[0,1]逼近样条(?)∈C[0,1]∩φ~*(m,q)。当n≥3时,存在f的最佳L_p[0,1]逼近样条(?)∈C^1[0,1]∩φ~*(m,q)。展开更多
Recently, Sun Yongsheng considered the approximation constant for the Cesàro means. The author gave the approximation constant for the typical means about the subclass of f（x）∈C2π under C norm. Now
文摘设L是常系数n阶线性微分算子,m∈N, 0=s_0<s_1<…<s_r<s_(r+1)=1是一组自由节点,在s_v处的重数是m_v≥1,sum from v=1 to r m_v≤m。广义样条 Φ~*(m,q)={φ|Lφ=0,φ∈C~∞(s_v,s_(v+1),v=0,1,…,r,且φ∈C^(n-1-qm_v)(s_v-δ,s_v+δ),δ>0适当小,v=1,…,r}本文证明了设f∈L_p[0,1],1≤p<∞,那末当n≥2时,存在f的最佳L_p[0,1]逼近样条(?)∈C[0,1]∩φ~*(m,q)。当n≥3时,存在f的最佳L_p[0,1]逼近样条(?)∈C^1[0,1]∩φ~*(m,q)。
文摘Recently, Sun Yongsheng considered the approximation constant for the Cesàro means. The author gave the approximation constant for the typical means about the subclass of f（x）∈C2π under C norm. Now
