Principal shift-invariant spaces with extra invariance nearest to observed data

• Autores: Akram Aldroubi, Ilya A. Krishtal, Romain Tessera, Haichao Wang
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 63, Fasc. 3, 2012, págs. 393-401
• Idioma: inglés
• DOI: 10.1007/s13348-011-0047-7
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• Resumen

  • Given a set of functions {\mathcal{F}=\{f_1, \dots, f_m\}\subset L^2(\mathbb{R}),} we construct a principal shift-invariant space V nearest to {\mathcal{F}} in the sense that V minimizes the expression \sum_{i=1}^{m}\|f_i-P_{V}f_i\|^2, among all the principal shift-invariant spaces with an orthonormal generator which are also translation invariant, or among all the principal shift-invariant spaces with an orthonormal generator which are also {\frac{1}{n}\mathbb{Z}} -invariant for some fixed {n\in\mathbb{N}}.