Abstract. In this paper wavelet packet bases are used for an estimation of the autoregressive Hilbertian processes operator. We assume that integral operator kernel can have some singular structures and estimate them by projecting functional processes on suitable bases. Linear methods for continuous-time prediction using Hilbert-valued autoregressive processes are compared with the suggested me...

Abstract. This paper is concerned with the numerical approximation of the minimizer of the continuous RudinOsher-Fatemi (ROF) model for image denoising. A new discrete total variation is proposed and the associated Hilbertian total variation denoising model is used to construct continuous piecewise linear functions that approximates the minimizer of the ROF model in the strong topology of L2(Ω)...

Let (ξn)n≥1 be the polygonal partial sums processes built on the linear processes Xn = ∑ i≥0 ai( n−i), n ≥ 1, where ( i)i∈Z are i.i.d., centered random elements in some separable Hilbert space H and the ai’s are bounded linear operators H → H, with ∑i≥0‖ai‖ < ∞. We investigate functional central limit theorem for ξn in the Hölder spaces H o ρ(H) of functions x : [0, 1] → H such that ‖x(t+ h) − ...

Let K be a countable separably Hilbertian field. Denote the absolute Galois group of K by G(K). For each σ ∈ (σ1, . . . , σe) ∈ G(K) let Ks[σ] be the maximal Galois extension of K which is fixed by σ1, . . . , σe. We prove that for almost all σ ∈ G(K) (in the sense of the Haar measure) the field Ks[σ] is PAC and its absolute Galois group is isomorphic to F̂ω. Mathematische Zeitschrift 224 (1997)...