CHARACTERIZATION OF L(P)-SOLUTIONS FOR THE 2-SCALE DILATION EQUATIONS

We give a characterization of the existence of compactly supported L(p )-solutions, 1 less than or equal to p < infinity, for the two-scale d ilation equations. For the L(2)-case, the condition reduces to the det ermination of the spectral radius of a certain matrix in terms of the coefficients, which can be calculated through a finite step algorithm. For the other cases, we implement the characterization by the four-co efficient dilation equation and obtain some simple sufficient conditio ns for the existence of the solutions. The results are compared with k nown ones.