Let P(D) be the differential operator generated by a polynomial P, and let U
P
2 be the class
of multivariate periodic functions f such that kP(D)(f)k2 6 1. The problem of computing the
asymptotic order of the Kolmogorov nwidths dn(U
P
2
, L2) in the general case when U
P
2
is
compactly embedded[r]