Artículo
A Characterization of Best φ-Approximants with Applications to Multidimensional Isotonic Approximation
Fecha de publicación:
08/2004
Editorial:
Springer
Revista:
Constructive Approximation
ISSN:
0176-4276
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Some properties of best monotone approximants in several variables are obtained. We prove the following abstract characterization theorem. Let ( , A, µ) be a measurable space and let L ⊂ A be a σ-lattice. If f belongs to a Musielak–Orlicz space Lϕ( , A, µ), then there exists a σ-algebra Af ⊂ A such that g is a best ϕapproximant to f from Lϕ(L) iff g is a best ϕ-approximant to f from Lϕ(Af ). The σ-algebra Af depends only on f . When ⊂ Rn and Lϕ(L) is the set of monotone functions in several variables, we give sufficient conditions on the geometry of to obtain a uniqueness theorem. This result extends and unifies previous ones. Finally, we prove a coincidence relation between a function and its best ϕ-approximant. Our main results are new, even in the classical Lebesgue spaces Lp
Palabras clave:
LATTICE
,
ISOTONIC
,
APPROXIMATION
,
RADON-NIKODIM
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Identificadores
Colecciones
Articulos(CCT - CORDOBA)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - CORDOBA
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - CORDOBA
Citación
Mazzone, Fernando Dario; Cuenya, Hector Hugo; A Characterization of Best φ-Approximants with Applications to Multidimensional Isotonic Approximation; Springer; Constructive Approximation; 21; 2; 8-2004; 207-223
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