In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q a...In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q and Kn(Bp(G),Bp(G))q are obtained for p=1 and ∞,1≤ q≤∞.展开更多
Let ? = {a +G*h|a∈R, h⊥1, ||h||_p≤1}, where G is a B--kernel. We obtain the exactvalues of the d_(2n)(B_p, L_p), d^(2n)(B_p,L_p) and δ_(2n)(B_p,L_p) for p∈(1,+∞)/{2}. Furthermore. weidentify some optimal subspac...Let ? = {a +G*h|a∈R, h⊥1, ||h||_p≤1}, where G is a B--kernel. We obtain the exactvalues of the d_(2n)(B_p, L_p), d^(2n)(B_p,L_p) and δ_(2n)(B_p,L_p) for p∈(1,+∞)/{2}. Furthermore. weidentify some optimal subspaces for d_(2n) and d^(2n) respectively, and construct an optimallinear operator of rank 2n for δ_(2n), from which we answer affirmatively Pinkus Conjecture,i.e. ?p≥q≥1, W_(2n)={a +sum from i=0 to (2n-1) a_iG(x-iπ/n)a,a_i∈R,sum from i=0 to(2n-1) a_i=0} is an optimal subspace ford_(2n)(?_p,L_p) for p=q.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10771016)the "985" Programme of Beijing Normal University
文摘In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q and Kn(Bp(G),Bp(G))q are obtained for p=1 and ∞,1≤ q≤∞.
基金Project supported by the National Natural Science Foundation of China.
文摘Let ? = {a +G*h|a∈R, h⊥1, ||h||_p≤1}, where G is a B--kernel. We obtain the exactvalues of the d_(2n)(B_p, L_p), d^(2n)(B_p,L_p) and δ_(2n)(B_p,L_p) for p∈(1,+∞)/{2}. Furthermore. weidentify some optimal subspaces for d_(2n) and d^(2n) respectively, and construct an optimallinear operator of rank 2n for δ_(2n), from which we answer affirmatively Pinkus Conjecture,i.e. ?p≥q≥1, W_(2n)={a +sum from i=0 to (2n-1) a_iG(x-iπ/n)a,a_i∈R,sum from i=0 to(2n-1) a_i=0} is an optimal subspace ford_(2n)(?_p,L_p) for p=q.
