EXACT AND ASYMPTOTIC ESTIMATES FOR N-WIDTHS OF SOME CLASSES OF PERIODIC-FUNCTIONS

Let W(p)r: = {f\f is-an-element-of C(r-1)[0, 2-pi], f(i)(0) = f(i)(2-pi), i = 0,...,r - 1, f(r-1) abs. cont. on [0, 2-pi] and f(r) is-an-element-of L(p)[0, 2-pi]}, and set B(p)r: = {f\f is-an-element-of W(p)r, parallel-to f(r) parallel-to p less-than-or-equal-to 1}. We find the exact Kolmogorov, Gel'fand, and linear n-widths of B(p)r in L(p) for n even and all p is-an-element-of (1, infinity). The strong asymptotic estimates for n-widths of B(p)r in L(p) are also obtained.