Probabilistic and average linear widths of sobolev space with gaussian measure in space SQ(T) (1 ≤ Q ≤ ∞)

Probabilistic linear (N,δ)-widths and p-average linear N  -widths of Sobolev space W2r(T), equipped with a Gaussian probability measure μ, are studied in the metric of Sq(T)(1≤q≤∞),Sq(T)(1≤q≤∞), and determined the asymptotic equalities: λN,δ(W2r(T),μ,Sq(T))={(N−1)r+ρ2−1q1+1N⋅In1δ, 1≤q≤2,(N−1)r+ρ2−1q(1+N−1qIn1δ, 21,andSq(T) is a subspace of L1(T), in which the Fourier series is absolutely convergent in ℓq sense.