Coefficient Quantization in Banach Spaces

2006/06/13 by S. J. Dilworth, Dilworth, S. J., Edward Odell +5
Mathematics · #Advanced Banach Space Theory #Mathematical Analysis and Transform Methods #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.math/0606317

Abstract

Let (e_i) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a `finite alphabet'. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c₀.

Citations

• The distortion problem

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