ASYMPTOTIC EXPANSIONS FOR FOURIER-TRANSFORM OF SINGULAR SELF-AFFINE MEASURES

Singular continuous self-affine measures invariant with respect to som e stochastic dynamical systems generated by a finite set of affine con tractions on the axis are studied. The Hausdorff dimension of their su pport and leading terms of L2-norm asymptotic of the corresponding cut -off characteristic function are computed. It is shown that the power- law behavior multiplied by some oscillating functions of a logarithm o f a cut-off parameter for these terms is typical. The inverse reconstr uction problem of the invariant measure from the high-frequency behavi or of its characteristic function is discussed. (C) 1994 Academic Pres s, Inc.