A minimizing property of best monotone approximants on their level surfaces

• Autores: F.D. Mazzone
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 146, Nº 1, 2007, págs. 71-86
• Idioma: inglés
• DOI: 10.1016/j.jat.2006.10.002
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• Resumen

  • In this paper we show that a best monotone -approximant g on the cube (-1,1)n to a continuous and bounded function f is a best monotone -approximant on the level surfaces of g with respect to certain n-1-dimensional measure. This measure is mutually absolutely continuous with respect to the n-1-dimensional Haussdorff measure.