Work

On simultaneous density order from shift invariant subspaces in Sobolev spaces

Year: 2025

Type: article

Abstract: The notion of simultaneous approximation order (m, k) from shift-invariant subspaces in Sobolev spaces was introduced in the paper by Zhao (1995). Moreover, a characterization of those principal shift-invariant subspaces that provide simultaneous approximation order (m, k) was proved there. In this note, we prove another characterization using dilated by some adequate expansive linear maps of a shift-invariant subspace. In addition, we introduce the notion of simultaneous density order (m, k) and give necessary and sufficient conditions on a shift-invariant subspace to have a simultaneous density desired. To give our conditions, we shall explain the behavior on a neighborhood of the origin of the Fourier transform of the generators of a shift-invariant subspace. For this, we will use the classical notion of approximate continuity.

Source: Journal of Approximation Theory

DOI: 10.1016/j.jat.2025.106147

Authors: Ch. Boukeffous, A. San Antolín

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,910

Funders: Ministère de l'Enseignement Supérieur et de la Recherche Scientifique, Ministerio de Ciencia e Innovación

Award: G4032205190