Equivalence of A-Approximate Continuity for Self-Adjoint Expansive Linear Maps

@article{Antoln2007EquivalenceOA,
title={Equivalence of A-Approximate Continuity for Self-Adjoint Expansive Linear Maps},
author={A. S. Antol{\'i}n and S. R{\'e}v{\'e}sz},
journal={arXiv: Classical Analysis and ODEs},
year={2007}
}

Let A be an expansive linear map from R^d to R^d. The notion of A-approximate continuity was recently used to give a characterization of scaling functions in a multiresolution analysis (MRA). The definition of A-approximate continuity at a point x - or, equivalently, the definition of the family of sets having x as point of A-density - depend on the expansive linear map A. The aim of the present paper is to characterize those self-adjoint expansive linear maps A_1, A_2 for which the respective… Expand