Almost sure convergence of smoothing Dm-splines for noisy data.
Limiting behaviour of intrinsic seminorms in fractional order Sobolev spaces
We collect and extend results on the limit of as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and is the intrinsic seminorm of order l+σ in the Sobolev space . In general, the above limit is equal to , where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.
Fonctions spline par moyennes locales sur un ouvert borné de
Sur la convergence de D-splines d'ajustement pour des données exactes ou bruitées.
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