Abstract: | We establish that, for p ∈ 2, ∞), q = 1 or p = ∞, q ∈ 1, 2], the classes W
prof functions of many variables defined by restrictions on the L
p-norms of mixed derivatives of order r = (r
1, r
2, ..., r
m) are better approximated in the L
q-metric by periodic generalized splines than by generalized trigonometric polynomials. In these cases, the best approximations
of the Sobolev classes of functions of one variable by trigonometric polynomials and by periodic splines coincide.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1011–1020, August, 1998. |