Average sampling numbers of multivariate periodic function spaces with a Gaussian measure.

In this paper, we study average sampling numbers of the multivariate periodic function space L ̊ 2 with a Gaussian measure μ in the L q metric for 1 ≤ q ≤ ∞ , and obtain their asymptotical orders, where the Cameron–Martin space of the measure μ is an anisotropic periodic Sobolev space. Moreover, we show that in the average case setting, the Lagrange interpolating operators are asymptotically optimal linear algorithms in the L q metric for all 1 ≤ q ≤ ∞ . This is different from the situation in the worst case setting, where the Lagrange interpolating operators are not asymptotically optimal linear algorithms in the L q metric for q = 1 or ∞ . [ABSTRACT FROM AUTHOR]