Title: Harmonic analysis and algorithms for fractal IFS L2 spaces via infinite products of projections.

Abstract: We present new results at the cross roads of spectral theory for operators in Hilbert space, optimization, large sparse systems, geometry of fractals from iterated function systems (IFS), and new results in fractal harmonic analysis. In detail, we present a new recursive iteration scheme involving as input a prescribed sequence of selfadjoint projections. Applications include random Kaczmarz recursions, their limits, and their error-estimates.