Triangular constellations in fractal measures

Scattering on fractal measures

Abstract. We study the one-dimensional potential-scattering problem when the potential is a Radon measure with compact support. We show that the usual reflection and transmission amplitude r(p) and t (p) of an incoming wave eipx are well defined. We also show that the scattering problem on fractal potentials can be obtained as a limit case of scattering on smooth potentials. We then explain how...

Modular Fractal Measures

A notable example of a discontinuous-everywhere function that is not traditionally integrable, yet, when properly defined, can be integrated, is derivative of the Minkowski Question Mark function. Some subject matter overlaps that of [6]. This paper includes numerical results for the Fourier transform of the measure, its Mellin transform, and Poisson kernel. This document is a research diary no...

Lattice Models and Fractal Measures

XXX OBSOLETE XXX HALF-BAKED XXX The ideas described herein are confusingly presented, and are half-baked, incomplete, incoherent. Essentially all the ideas herein are presented more sensibly, more coherently in other papers on this website. Much of what was originally in this paper has been edited out, and moved to another paper, which presents the ideas in a much clearer fashion: see [9]. XXX ...

Fractal Components of Wavelet Measures

We compute the Coifman-Meyer-Wickerhauser measure μ for certain families of quadrature mirror filters (QMFs), and we establish that for a subclass of QMFs, μ contains a fractal scale.

Fractal Measures for Parabolic Ifs