n-WIDTHS OF SOME CLASSES OF PERIODIC FUNCTIONS

Let p = {a +G*h|a∈R, h⊥1, ||h||p≤1}, where G is a B-kernel. We obtain the exactvalues of the d2n（Bp, Lp）, d2n（Bp,Lp） and δ2n（Bp,Lp） for p∈（1,+∞）/{2}. Furthermore. weidentify some optimal subspaces for d2n and d2n respectively, and construct an optimallinear operator of rank 2n for δ2n, from which we answer affirmatively Pinkus Conjecture,i.e. ?p≥q≥1, W2n={a +sum from i=0 to （2n-1） aiG（x-iπ/n）a,ai∈R,sum from i=0 to（2n-1） ai=0} is an optimal subspace ford2n（?p,Lp） for p=q.

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.