Title

A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS 𝐿2 spaces

Document Type

Article

Publication Date

Summer 5-25-2020

Publication Title

Advances in Operator Theory

Department

Mathematics & Statistics

Abstract

We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as “the” Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are central to spectral theory of operators in Hilbert space, to optimization, to large sparse systems, to iterated function systems (IFS), and to fractal harmonic analysis. 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.

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