Haar bases for L-2(R-n) and algebraic number theory (vol 57, pg 181, 1996)

Wr correct an error in the proof of Theorem 1.5 in Lagarias and Wang (J. Number Theory 57, 1996, 181-197). We also give a Strengthened necessary condition for the existence of a Haar basis of the specified kind for every integer matrix A that has a given irreducible characteristic polynomial f(x) with textbackslash{}f(0]textbackslash{} = 2 A Potiopa (Master's thesis, Siedlce University, 1997) Found that the expanding polynomial g(x) = x(4) + x(2)+2 violates this necessary condition, Thus there exists a 4 x 4 expanding integral matrix A of determinant 2 and characteristic polynomial g(x) which has no Haar-type wavelet basis using an integer digit set D subset of or equal to Z(4). (C) 1999 Academic Press.