On Bergman space zero sets. Editors’ comments on the article by Vaughan Jones

Abstract

This article has two purposes. The first one is to describe what the Editors know on how and when Vaughan Jones worked on the subject of the article published in the same volume. The starting point, in the late 1980’s, was his fascination for a formula giving Murray–von Neumann dimensions of Hilbert spaces of unitary representations of Fuchsian groups. Over the years, he discovered surprising relations of these dimensions with other domains of mathematics. The second purpose is to expose with some details a subject which plays an important role in Jones’ article: the irreducible projective unitary representations of ${\mathrm{PSL}}_2(\mathbf{R})$, which constitute a continuous family known as the discrete series, and which have interesting restrictions to various discrete subgroups of ${\mathrm{PSL}}_2(\mathbf{R})$.