Douglas A. Wagner | Searcharxiv

arXiv2021

Approximately Multiplicative Decompositions of Nuclear Maps

We expand upon work from many hands on the decomposition of nuclear maps. Such maps can be characterized by their ability to be approximately written as the composition of maps to and from matrices. Under certain conditions (such as quasidiagonality), we can find a decomposition whose maps behave nicely, by preserving multiplication up to an arbitrary degree of accuracy and being constructed from order zero maps (as in the definition of nuclear dimension). We investigate these conditions and relate them to a W*-analog.

math.OA↗

arXiv2015

Asymptotics of the energy of sections of greedy energy sequences on the unit circle, and some conjectures for general sequences

In this paper we investigate the asymptotic behavior of the Riesz $s$-energy of the first $N$ points of a greedy $s$-energy sequence on the unit circle, for all values of $s$ in the range $0\leq s<\infty$ (identifying as usual the case $s=0$ with the logarithmic energy). In the context of the unit circle, greedy $s$-energy sequences coincide with the classical Leja sequences constructed using the logarithmic potential. We obtain first-order and second-order asymptotic results. The key idea is to express the Riesz $s$-energy of the first $N$ points of a greedy $s$-energy sequence in terms of the binary representation of $N$. Motivated by our results, we pose some conjectures for general sequences on the unit circle.

math.CA↗