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ON THE ERRORS OF MULTIDIMENSIONAL MRA BASED ON NON-SEPARABLE SCALING FUNCTIONS

BARBARA BACCHELLI

Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy

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MIRA BOZZINI

Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy

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MILVIA ROSSINI

Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy

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https://doi.org/10.1142/S0219691306001397Cited by:3 (Source: Crossref)

Abstract

In this paper, we deal with two different problems. First, we provide the convergence rates of multiresolution approximations, with respect to the supremum norm, for the class of elliptic splines defined in Ref. 10, and in particular for polyharmonic splines. Secondly, we consider the problem of recovering a function from a sample of noisy data. To this end, we define a linear and smooth estimator obtained from a multiresolution process based on polyharmonic splines. We discuss its asymptotic properties and we prove that it converges to the unknown function almost surely.

Keywords:

AMSC: 65D07, 65D10, 41A15, 41A30, 42C40

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