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Off-diagonal decay of matrix factorizations

Student-Run Applied & Math Seminar

Speaker: Tim Wertz, University of California, Davis
Location: 2112 MSB
Start time: Fri, Feb 1 2013, 12:10PM

An important non-commutative generaliztion of the famous Wiener's Lemma states that under certain conditions the inverse $A^{-1}$ of a matrix $A$ will inherit the off-diagonal decay properties of $A$. In this paper, we investigate whether this Wiener property extends to matrix factorizations. For example, given the QR-factorization $A = QR$ of a bi-infinite matrix $A$, where $A$ belongs to some Banach algebra $\mathscr{A}$ which characterizes its off-diagonal decay, do $Q$ and $R$ also belong to $\mathscr{A}$? We will answer this question for the most important matrix factorizations.

Pizzas and soda will be served.